bokaboi:
This is what I’m imagining with the lighting setup.
http://digibeno.sharkserve.com/StageDesign.png
So you'll be mounting the strips on the back wall then? That could come in handy if you can punch through the wall and run cables either inside, or behind it.
bokaboi:
Controller Desk:
This is what I have in mind for the controller desk.
http://digibeno.sharkserve.com/ControllerBox.png
I’ve also added a ‘Master’ channel. If the Master ‘Take Over’ switch is thrown, ALL channels will follow the settings on the master channel.
Consider the possibility of having the master channel, not only take over color, but also have the ability of taking over the "current settings" as is and controlling brightness/gamma as it were. For example, if you have a specific setting already in place (take your own stage design picture in mind) and simply tell the master to dim them, and not override the color as well.
bokaboi:
I think an LCD display may be a bit advanced? I’m not too sure what data I’d have it display. I’ve tried to make the desk layout as logical and fool proof as possible. Maybe V2 will have programmable presets 
However for now, I’ll probably leave it out unless you can convince me otherwise 
It depends on what you'd want to display on the LCD, and who is it for. If the person (or persons) driving the light booth don't have a clear view of the stage, an LCD will come in very handy. On the other hand, if they can see the stage, even when there are a hundred people in front of it, then it comes down to what that person needs to see that can't otherwise be done unless they are on stage, next to the strips. Though simple things like 'STRIP 1 : ON|OFF', STRIP 2 : ON|OFF' just to indicate whether they are on or off might be fun. During day time when it's hard to see whether a particular strip is completely off, or whether it's on at 1%, a visual indicator on the LCD panel might come in handy. You could also wire in your smoke machine to see whether it's on, heated, and ready, out of fluid, etc., etc. LCDs have their place in a project, you just have to figure out what for.
bokaboi:
Questions:
Is this still do-able?
Absolutely.
bokaboi:
Is this a job for a single Mega, as apposed to four Uno’s?
That would depend on how you want to control the strips. I have done both. If I take a single Uno clone (basically the 328P chip), I can wire 10 individual strips to that (10 LEDs each without any additional current boosting hardware) and bit bang my way through them and still get great results. On the other hand, that severely limits what else I can do with that one single controller, like adding control lines for something like your control deck. At that point I have a choice of either sticking with the 328P and just use more of them linked together, or move up to a 1280 or 2560 (which is the Mega realm).
Also, it would depend on the specific strips you plan on getting, whether they are simple RGB full color strips, or whether they are RGB addressable strips. The difference is, the first one will display one color across the whole strip, while the other allows you to display different color on each individual pixel on the strip. The first one takes very little to do, where the second one needs a bit more oomph to drive. For an example of what you can do with addressable strips, here's my latest project where I have 10 328Ps working in tandem, each one has 2 strips attached. The reason they're 10 of them, and not a single one, or maybe two of them, was because this was originally meant to be for a parade where kids would've worn them (two strings per kid, one controller each.) And they all change sequence through RF signals. http://www.youtube.com/watch?v=-3ex1k8f_Nk
bokaboi:
Latency, keeping in mind that I’ll want to be able to tap the strobe button to a beat from live music; will there be any latency?
Manual tapping, or automatic, beat sensing software, that will strobe the lights? Manual tapping the latency is however fast you can do it. 
Software sensing takes a bit more, but should still be doable.
bokaboi:
Moving forward:
Where to from here?... I have a logical mind, I can usually understand coding syntax once I have the code – but I can’t write it from scratch. What I was hoping to find perhaps users, or an archive of code, that would be able to do parts of this project. Then I’d mash it all together whilst teaching myself. Are there any places you would recommend I should look at?
Think about everything everyone's told you so far, and start writing out what you want to accomplish in terms of 'how you want them controlled, as in, running wires from where to where, where's the control box going', 'what kind of strips do you want to work with', 'consider power/current consumptions', 'specific hardware' ...
Also, keep in mind that you are not forced to use a ready made Uno or Mega, you can design your own board with everything you need. Those lights in the video I linked above? That's a custom board running an Arduino Pro Mini bootloader (so it behaves like a regular Pro Mini). See attached picture.
