I have all my hardware together, Trinket with LiPo battery, OLED screen, and inputs. I put together a custom board for the inputs, just an 8-way mini joystick and 2 tact switches for the buttons. Here's the switches mounted to a protoboard that I hacksawed down to a more manageable size:

I have the OLED set up on a breadboard for testing and prototyping with an Arduino, although I'm gonna port the code to the Trinket. I'm currently having a problem making the Trinket show up in my USB device tree, although I am reasonably certain I can fix this soon.

The battery and charging circuit work fine, the pre-loaded demo of the LED fading runs for a little over 24 hours off the 500 mAh LiPo.

Current to do list:

1. Make USB work

2. Get screen output from the Arduino or the Trinket

3. Solder the buttons and joystick to some of the outputs

4. Port the games that run on TVOut to my setup

5. Make some original games, or ports of my Atari favorites