Quick release baseplate for Ricoh GR series?

I'd like to use a quick release baseplate system with a backpack strap mount for my Ricoh GR IV. I think that's ideal when hiking/backpacking.

However, as the GR is such a small camera, all baseplates are uncomfortably large. The most common size seems to be about 38mm square; there are plenty of options in that size. Including mounting accessoires such as quick release strap mounts. But 38mm is way too large for the GR.

Falcam has a 22mm system that, on paper, would fit well (aside from blocking the SD/battery cover but that's to be expected). But I can't find a backpack strap mount for it.

Does any of you have a good solution for this?