How do I make a recording of a group of people playing a tabletop rpg?

I heavily advise against using lavalier mics unless the people wearing them have incredible microphone discipline. Especially in a setting in which you are prone to forget the recording situation like a TTRPG session, it's way too likely that people will touch the mics, hair, beards or clothes will scratch them or that cable connections will be interrupted. While you can fix some of that in post production by just cutting the audio whereever there is no dialog, often dialog itself will be impacted aswell.

Instead I would advise a solution like the one that can be seen in the below video, if it's at all feasible for you.

This is a setup for the exact purpose of capturing dialog during TTRPG sessions and mitigates the typical problems of a lavlier mic setup.

Your strategy would be the best idea. You may get some bleed between the mics, but your room acoustics may be an issue. The more you put into deadening the walls with sound insulators, the better the final product. Even if it is a few shelves with books and such on them...it will help with the reverberations.