The LIR2032 coin cell batteries that I used with this device so far are not the perfect solution. Sure, they are easy to get and replace, don't look nearly as scary as the aluminium pouch of the LiPo batteries, and actually have enough electricity to play for almost an hour, but they also have down sides: they are very slow to charge, 40 minutes of play time is not nearly enough for the more boring travels, and they don't look very well on the back of the device.

So I looked around for a different battery. I has to be:

• standard, so that I can tell users what battery they need to get,
• larger and capable of faster charging,
• easily obtainable and cheap,
• protected from over-discharge,
• flat and roughly the same size as the device,
• physically robust.

That actually narrows the possibilities considerably, but I had an idea: let's use a battery from a cellphone — not a smartphone battery, those are too big and expensive, but a battery from one of the popular dumb phones. Nokia used to be a popular brand, so I'm sure there are a lot of cheap Nokia batteries I could use!

Looking around I found the "Cellphone Knowledge Base" wiki, and there I found the two battery models that fit: BL-5B and BL-4S.  I ordered one of each, and they arrived recently. The bigger and older one, BL-5B, arrived first:

It's a bit of a tight fit, exactly the same height as the µGame. But the connector it uses let's me improvise something from goldpins, so it works pretty well:

You can see the holes are not exactly right (I didn't have the dimensions when I designed the PCB) but they are close enough for this to work. Today the second battery arrived, and I actually like it a bit more. It's smaller but thicker, and it doesn't cover the mounting holes:

The connector is a bit more tricky — I think I will simply solder it to the battery pads, after attaching the battery with 2-sided tape. It's supposed to be a prototype kit anyways.

@MatejEusk is working on designing a 3D-printed case for this, it might work a little bit better with those batteries then.