If as you say, her resources are divested long ago, and Mom's only income is Social Security and a pension, I think you may find that there are ways to deal with that and her still not to be disqualified for skilled nursing facilities through medi-Cal. It sounds as though your medical experts feel she needs this type of care.
As to whether they do a good job with memory care issues, it was my experience that on any and all issues, how well these facilities do has everything to do with the back up people for this individual. In my personal situation, the position of having my parent in the care facility was a tremendous relief to me in that I was able to be there with her every day, overseeing her care, but at the same time, I was not solely responsible for every single thing that happened with her, every lifting, every change, every meal, every medication. It was by no means "dumping" my parent in a nursing home and running away, and in spite of what her visualization of such care would be, she was actually more engaged and less bored in a place where more was going on.
But it sounds as though you have truly exhausted yourself, and there is no real way to force another family member to come through as you would like. Karmic justice for such things is spectacularly slow in coming sometimes. So you must accept that you cannot martyr yourself much longer and explore other care options for her. As has been said, you will always know that you have been the one who did the right things.