The boards from Aisler just arrived, so I could assemble the first prototype. Almost all fits, except for the resistor next to the battery charger, for which I had to cut a small hole in the plastic of the battery holder. Fortunately there is room to move it.
Next is programming the little thingy. I got the bootloader burned on it:
Now I need to compile some firmware and see how those touch pads work. I still don't have the LIR1202 batteries for it, so I can't test if it actually runs on the battery — it's possible the battery will be too weak for the display. The CR1202 definitely is too weak.