OK. So after spending 9 hours recreating the whole game from scratch in Godot 3.5 (older engine version), I managed to get it running... but there are way too many bugs to fix for it to be in an acceptable condition.
Unfortunately I can't spend any more time on this "engine downgrade" experiment to get the game to work on older hardware. I really didn't expect there would be sooooo many changes between versions and that it would take so long to get to this half-done point.
If I manage to get some free time from my other projects, I'll try to get back to this and fix the bugs, but it's very low priority right now.