@gratia I don't know if this is even a good suggestion and one by the readers the may sound ludicrous, but in reading your "toilet time" post, I couldn't help but wonder if one of those large plastic inserts the doctor or hospital gives us to fit inside the toilet rim when we take a stool specimen, would be appropriate when she goes to the bathroom. This way, her stool doesn't clog up the toilet, and when she uses toilet paper, she stuffs that in the plastic insert piece along with the poop OR you give her a plastic trash bag to put the toilet paper inside (if she remembers to do it). Then you can dump it however you see fit. It will stop clogging up the toilet. May appear to be an extra step, but plunging away with a migrane becomes many extra steps and a lot of work to toilet overload.
Best, Karla