@mariaparker here you go: Moleskine Journey Travel Light Battery Replacement
Wouldn't bother buying the thing, if not for your article. So, thank you!

Thank you for the teardown. It looks manageable.

Note 1: since there are Phillips-head screws on the front, you were, quite obviously, on the right track. I am pretty sure that the case is being welded right after the molding process, before the installation of the circuitry.
Note 2: my guess is, the things that constrained you were the battery adhesive, combined with short wires. There is no such problem until you glue the battery in. The wires are pre-soldered, and the package is ready to go.

I am going to try one myself. Here are some guesses:

1. As always, pre-heating the device would soften any adhesive. Both the reflector and the battery should come out easier.
2. If the battery is still stuck, while the reflector comes off, it is a good time to desolder as much as possible. PCB on its own should come out easily.
3. As for the replacements, 352025 are the dimensions, 3.7V is universal between such batteries, and a little charging-controller PCB inside a battery is a must.
4. Epoxy!