The Duty Cycle and Power Consumption of My Project:
The Atmega328P-PU spends 16 seconds in Power Down Sleep before waking up to turn on a real time clock running at 3V3 supplied by a digital pin on the Atmega. The Atmega checks the time and if there's nothing to do, it goes back to sleep again.
In total, my project spends 24 minutes per day active and powered up. This is broken down to roughly 30 seconds of activity three times an hour for around 16 hours per day.
When my project is active, the first stage is to send out a data transmission over RF at approx 0.5W at 3.7V. This consumes a total of around 140mA according to my bench supply.
The second stage of activity is to send an SMS message. This consumes around 120mA at 3.7V.
The RF related modules are the first devices to be powered up, they do their thing then the power switches over to the GSM. I did this to prevent any interference between modules such as the GSM trying to communicate with the network in close proximity to the RF transmitter while it's trying to send data. It just seemed like the most sensible approach.
The Power Source for my Project:
Initially I was using a 12V Sealed Lead Acid battery to power my project but they didn't perform as expected so I'm next trying Li-Ion which will be around 8V (which I'm currently simulating with my bench supply until I'm sure thats the way I'm headed and build the battery pack).
Early prototype designs of my project were based on 12V and used 12V relays. Now I'm using 8V, I'm using 5V relays which are technically being over-driven BUT according to the datasheet, they can work on 75% of their rated coil voltage, up to 120% of the rated coil voltage and they seem to be working okay. No odd or erratic behavior noticed.
In the end, I will go with whatever battery source suits my project and will perform the best once I get the power management and supplies sorted and finalized. And this is the reason I decided to build the power supply as a separate entity because it's constantly changing based on tests and results observed / recorded.
My Ultimate Aim:
So in short, I want to have my Atmega permanently powered up at 3V3. I don't care how I achieve it just so long as the power consumption is as low as possible when the Atmega is asleep and drawing very little.
When it's time for the Atmega to wake up and turn on the modules, take sensor readings and transmit data etc. I'd like the Atmega to turn on the power supply for the modules and then be able to power up one lot of modules and then switch that same supply to another separate lot of modules.
While I'm initially more concerned about the amount of power consumed at sleep / standby (where the Atmega spends most of it's time), if I can save some power when the atmega is fully working and the modules are active, then that would be a bonus. Obviously I can't shave any power from the RF transmissions but if I could find relays that consume less current or an alternative, that's some power saved at least.
Looking at Alternatives?
So let us assume that I revisit the MOSFET idea.....
This is the circuit I was playing around with initially to turn on the power supply to my modules.
Also shown is my initial attempt at a 3V3 supply with the AMS1117 (ignore that).

I used a 2N2222 to turn on the MOSFET but for some reason, it the FET would eventually fail and be permanently on.
I'm open to look at and explore the idea of using MOSFETS again but it needs to be reliable.
And finally, what would be recommended in place of the MP1584EN to supply 3V3 to the atmega permanently which takes very little current / power when the Atmega is sleeping / in standby?
Also requested was the schematic for the power board I'm currently using which uses the relay to switch on the Buck Converter which puts out 3.7V...

It's not a very good schematic, I roughed it out quick just to prove the idea. I didn't want to go to the trouble of laying it all out nice and pretty when it could get ripped apart or scrapped at a moments notice.
It basically works like this....
Main Power EN is a pin from the Atmega which goes high to turn on a 2N2222 which turns on a relay.
The relay switches main power (in this case 8V) to the Buck Converter that puts out 3.7V to the modules via another relay which s not shown because that relay is on my main board not this power board.
Also on this power board, I was toying with a design I found on the internet for a battery voltage monitor based on a voltage divider and clamping diodes. I have not tested this yet. I found the design and included it in the schematic for later testing and experimenting.
I want to be able to monitor the battery voltage and include that data in the RF Data Transmissions and SMS messages. I went with this design because it apparently doesn't take much current from the battery while it's just sitting there doing nothing.
I did look at a Batt voltage monitor designs that could be switched with MOSFETS but there was a lot of conflict around the designs I found about how it would work or how it wouldn't work but with no real consensus on what it would do so I left that idea.
And that's pretty much it.
Thanks!