It can be hard to find a similar-sized battery. No worries, as more battery = more better.

I have experimented with paper mock-ups, and here are my findings.

The original battery thickness of 35 (3.5mm) is optimal, if not too large. The swollen old battery has marks from SMD components all over it. I say, go for 3.5mm or less. 40 won't fit.

The other dimensions are limited by the PCB posts and the size of the body itself. Without modifications, the biggest battery you can fit in is roughly 352330. Vertically or horizontally, the space is the same.

However, there is some sweet space, constricted by a post, marked in white. The post serves the purpose of stopping the micro-USB connector from being pushed inside. For my personal use, this should be superfluous.

Using a knife, I cut the post flush with the base. Now there is 15mm more battery space. Cool. Searching for a battery, I found a 302040 unit. It has 300mAh capacity and fits perfectly. Hopefully, the charging controller won't be against it. To be continued...