So I have managed to hook up a screen. It works and I learned a bit.
As you can see, I have an adafruit powerboost and a lipo battery attached. I had tried to hook the screen up directly and it worked, but the screen would flicker badly. I think it just didn't have the juice to run the screen with two AA batteries what it was doing is powering on and off. I added the PowerBoost which seemed to work better at first, after a few seconds of flickering, but it a little later it would flicker again, remaining stable for only a minute or so. So, I put the lipo battery in and removed the AA's and it works. The whole unit even powers off when I power of the game's main power-- it has a soft power button that you hold a few seconds to switch it off.
My main concern was the main board is only supposed to have 3v and I have 5v running through it, which could have been slowly frying the microcontroller, but I looked up it's data sheet and it has a range of 1.8 - 5.5v. I'll test putting just the battery in the circuit w/o the Powerboost to see if it's like the MintyPi and can run straight off the battery power. The screen nearly worked using two AA's so the lipo which is a bit more powerful (about 3.7v IIRC) might not need to be boosted to 5v.
EDIT: It works. So I only need the Adafruit Minilipo
Once that gets done, I'll also have to hook up the small amp I have and a speaker from one of those annoying birthday cards that plays a song.
EDIT: Got it working. This is a situation where a piezoelectric beeper would have been appropriate, but I got this speaker for free. The amp has an on/off volume knob and for some reason I just couldn't get it to shut off. I think it's because the power and signal were both coming from the main board so when the knob opened the circuit to shut off the amp, the signal circuit still sent enough power to keep it running. Shut off, it was louder than the lowest setting when on, which is weird. So I attached the speaker directly to the main board and it works. I could experiment some more with the amp or just save it for another project as it wasn't that loud, anyway. I may put a small switch in line with the speaker as a mute function because I'll bet the beeps get annoying.
I am still wondering it it'll be worth my time to rig some kind of switch that will shut off the screen and amp when you plug the until into a TV using the RCA jacks. I like the idea of the built-in screen and audio cutting out when you hook this up to a TV, but that may not be necessary and more trouble than it's worth. It may be impossible. I'll have to double check my circuit. I may have this drawing power from the screen, so shutting it off might break the whole power circuit.
In any case, this is a real sense of accomplishment. Once I get the innards working the way I like, I get to design and 3Dprint the case.