I finished connecting the 2.42 inch OLED display to the board. One difference this time: I added a 47uF capacitor across the 3.3v and GND to hopefully stop the display from dimming. And it appears to work! 

So the display, keyboard and BASIC are working. Currently just powered via the Nano's mini-USB socket. Still to come:

• External EEPROM (you can see it in the pictures but I need to 'reformat' the chip before it'll work properly)
• Buzzer (maybe switching to a flatter disc-type piezo sounder to take up less space in the tin)
• Power circuit with LiPo
• Possible switches for power and sound
• Fitting it all in the tin

So plenty to do! In the meantime, here are some images...