Also I noticed there's a whole section on yoga poses during menstruation! This seems particularly promising, as my previous attempts at home exercise have been derailed by aches and cramps before.

YMMV (as is always true with body stuff), but there are particular yoga poses which I've found actively helpful with menstrual cramps. Can babble about this if it'd be useful.

Plus slow yoga can just give you a nice option for a low-energy thing you can do when you're not feeling up for anything strenuous, for menstrual or other reasons.