In any case, hat-tip for empiricism! Very pro composting, wish it was safer, smaller, and easier to do at home.
Personally, my menstrual cycle has been 100% reusable since 2003, and I much prefer reusables to disposables on a comfort level. I mostly use cloth pads, but I use a cup sometimes also. I used to be the opposite - mostly cup, sometimes cloth pads.
Depends on how many people you have/how frequently you empty your bin? In my apartment, it's just me + my partner, and we empty our main trash about twice a week, using a regular shopping bag. Most of our waste is food waste (we have a food waste bin) or packaging (which can be recycled).
I, for one, would love to know the results of said experiment once you are satisfied that it has run it's course. Also, do you happen to have a link to the compostable bags? I gave up trying to find some that worked years ago.
I'm not sure how it works in your house, but in mine the small trash cans throughout rooms are almost entirely filled with compostables like paper towels, tissues, floss, and tampons (I've gotten in arguments about whether floss and tampons will actually compost - that experiment is currently running in our backyard). So you could just Chuck those bags straight into the compost bin, if your city has it. If it doesn't, maybe not a good idea cause the bags will just disintegrate at the landfill and blow trash everywhere.
Really the answer here is convince local government to do recycling and compost collection and make an effort to purchase and cook in such a way that as little goes into the landfill bags as possible. I recently visited my childhood home in Texas and felt super gross when my only option for a can of Coke I had finished was chuck it straight into the bin... I've been thinking a lot lately about how stuff just is accumulating in landfills. Maybe it's my SF instincts screaming "that's a couple square miles of great real estate if it wasn't full of trash!" Lol.