It is preferred to have a separate supply for inductive loads.
One would expect someone designing a circuit such as yours to have an oscilloscope to look at the noise level on the supplies. Barring that, typically, you start adding large value electrolytic caps until the noise is suppressed. In addition, ALL
digital chips should have 0.1uF decoupling caps
as physically closet to the power pins as possible.
I quickly sketched together a diagram that I hope you can see the concepts.
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The black circle is what some call a "star" common. The concept is the high current devices and the low current devices CANNOT ever share a common. What isn't shown is at the "star" there is capacitive filtering for both the high current and low current, making it the 12V (hi current) and 5v (low current) somewhat independent.
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The is a physical separation between the high current (solenoids etc) and the low current wires.
The plastic housing is more of a challenge.
If I were to do this I would consider two aluminum boxes. The boxes would be bonded at one side and that would become the system common.
I'm assuming:
- You will only be building one of these for your testing (perhaps a 2nd)
- You have little or no test equipment to test for susceptibility to noise.
- Finishing and troubleshooting is on some sort of schedule, making performance out of the gate important.
I have done a fair amount of testing in the desert (not rockets).
- Dust everywhere
- Animals are not your friend.
- It does rain and can come upon you quickly. We tested in the summer, could be different at different times of the year.
- Shade is your friend and you equipment's friend.
- Troubleshooting in the heat is not fun.
@fawltyplay this is where you get confused because 2 people who claim to know what they are doing (Paul_B and myself) disagree. Paul has been here a long time and I do not doubt that he knows what he's talking about, I too claim to know what I'm talking about!
At the time I commented I didn't know what power supplies you had so my answer was partly based on a guess about what you have, but now I know. As Paul suggests, that terminal is to connect the safety earth from the mains supply to the power supply, and you should do so for safety (nothing to do with noise). I would expect that the earth terminal is connected to the metal case of the PSU but not connected to the output at any point. Where I disagree with Paul is that I would connect that terminal to the star grounding point we have been discussing. I contend it would not introduce any noise because there is no complete circuit that includes that connection and the wider world. However, if you do connected it then you MUST NOT connect any other part of the circuit to safety earth anywhere by any means because if you do there will be a complete circuit, or earth loop, and that will introduce the noise Paul is concerned about. Note that the only reason for making that connection is safety. If you make it and suspect noise you can disconnect it to see if it makes a difference.
Yes, that is a recipe for noise problems. A basic principle you have to adhere to if you are concerned about noise is that the net current in a bundle of wires (cable) is zero. So you consider how the current goes from its source, to the load and back and those 2 (at least) wires should be bundled together. Think of the mains cable, the live and neutral are together, that is convenient but also it is good electrical practice, the net current in the cable is zero. Another way to consider this is you avoid loops at all costs. The next thing is to keep cables doing one job physically separate from cables doing a different job, so in this case wires with digital signals should be separate from wires with analogue signals, but to repeat the above they should be bundled with their respective 0V / ground wires.
Note: Unless I missed something you have a system in the middle of the desert being run by a generator set. So unless you drive a grounding rod into the desert sand you don't have an earth ground. You do however have to pay attention to how the gen set is wired. If it is floating with regard to its frame, something must be connected to the frame to keep the generator output from floating causing issues with safety and noise.
Software:
You should make sure you are not switching a solenoid immediately before taking a reading.
I missed that John. I wonder how that might complicate things, the safety earth should come from the generator I guess and be connected to the frame and the neutral at the generator.
I'm really not familiar with such a configuration. However I know folks have been camping with generators for years and I've not heard of any problems. Except perhaps from the bears or undead 
I'm not sure how to communicate to the OP how easy it is for changing voltages to couple from one wire to the next. Here in the US we have 120V household LED bulbs. I saw on some video of someone connecting a LED bulb to a 6 foot extension cord. Then laying it next to another cord that was plugged into the mains. The bulb lit up noticeably with no galvanic connection to power.
I tired it myself and could reproduce it easily, and that was 60Hz. It's much easier to couple fast changing signals to wires you don't want those signals on.
Earth GND is not for equipment. It is a safety feature. If the equipment was contained inside a
plexiglass enclosure that prevents anyone from touching the power supply chassis then you
wouldn't even need an Earth GND. I've run plenty of circuits off 2-wire supplies and never had
any problems. The star Grounding is another story. That is always a good practice for commonly
grounded circuits.
And what sort of safety is that?
Which is why I caution that all this reverence for "star grounding" is entirely misguided. 
I wish I did. We've been working mostly remotely and seeing as I have the hardware but no oscilloscope until campus opens in a few weeks I'm just doing my level best to be proactive for now.
Understood. This should be very easy to add at the screw terminals on each PCB.
All of these assumptions are correct, especially troubleshooting in the heat. We do have access to oscilloscopes when campus re-opens, but as we are not allowed to do any pressurized testing there the solenoids may not operate properly as they have an input pressure requirement.
We have done pressurized testing of the entire system in the past. Things were quite noisy, and we weren't running off of a generator but rather house wiring at the time. Things were "fine" and nothing impeded us from controlling the physical system, and the data was usable but not pristine. We also have concerns about the TC circuits in particular. This plus an interest in learning the proper way to do things motivates the post.
When you say they cannot share a common, do you mean that the current return paths should never be downstream of each other but rather be separate branches? I.e.
_____[Filter cap]________[High current circuits]
GND______/
\_____[Filter cap]________[Low current circuits]
as opposed to
[Low current circuits] [High Current circuits]
GND____[Filter cap]_______/__________________________/
Edit: I don't mean to imply that the filter cap goes between circuit GND outputs and the system GND, just want to illustrate its relative location.
The only other confusing part of the diagram for me are the GNDs near the busses you sketched that seem redundant given the presence of the star GND connected to the busses?
I see. Thanks for the explanation. Will certainly try both when able. The generator seems to not be floating with respect to its frame.
Cool! I will lengthen wires and find a way to route them so they don't cross over each other.
How long is "immediately"? Currently the MCU ships data as soon as it has it as fast as it can. We manage about 40SPS currently. That would be much higher if the sampling of the ADCs was faster. I haven't looked into that just yet. I would intuitively think with that low of a sampling frequency there should be low-to-no impact on the sampling if I can space things out by a few ms.
Makes sense. It's been some time since I took an E&M course but I remember exercises involving induced currents in parallel wires due to magnetic fields changing at the moment of a switching action. What is the common/best practice way to avoid this, other than distance?
Side note, I'm glad to see this much discussion. Thanks everyone for all your input!
Yes this is correct.
Makes sense. It's been some time since I took an E&M course but I remember exercises involving induced currents in parallel wires due to magnetic fields changing at the moment of a switching action. What is the common/best practice way to avoid this, other than distance?
Grounded shielding around the different wires. Perhaps you could use EMT conduit or simple copper water pipe. The conductive conduit/pipe will completely squelch the E field. It will severely reduce the magnetic field (although it is not magnetic.) due to the eddy currents that are created in the conductive material.
Both options look to be about the same cost. If I understand correctly the wires which are most important to isolate are:
Wires running from PTs to the PT boards and then to the ADCs.
Wires running from TCs to the TC boards and then to the ADCs.
Wires running from solenoids to their power sources.
This should put some things to rest.
Its difficult to say the "important" ones are limited to those you listed. However those you listed are definitely the most sensitive.
You should think of the noise as no longer being in the wire but also around the wire(s). Also the "dirty" wires can be anything connected to the solenoids or other high current devices.
BTW the conduits should be grounded only at the "star" connection.
We didn't talk about filtering. Add a 100µF in parallel with a 0.1µf ceramic at the star to the 12V power and the 5V power. Likely other filtering will be needed but I can't point where at the moment.
You could also use aluminum tubing from Home Depot if they have any instead of the EMT or copper. Probably would make a nicer package as they are mostly anodized silver.
Perhaps I'm misunderstanding his explanation but sending EMI filter ground to the chassis / safety ground is not an acceptable method to contain EMI.
This used to be done on old power supplies but today they will trip GFI devices. We had a 20V 20A HP supply that would trip the GFI's on our test stand.
The safety that comes from making sure there is a safe return path should the circuit inadvertently become connected to the live of the mains supply.