I posted back in January, and finally was able to get back in touch with Amex today after they had emailed me saying they had an update to my dispute.
In short, for all of the Square / Toast items, they said they have re-coded the restaurants so that way when I (or anyone else) goes to them, it should work correctly. I haven't yet tested this as I had all but quit using my card, but it was a very encouraging response.
For some items that credited as restaurant for CSR but were in hospitals, airports, etc. they gave me one-time "courtesy" credits for most of them, though a couple they said they couldn't do. So it's frustrating how it's very different (and more restrictive) than Chase, but I felt they mostly at least tried to work with me.
I have an outstanding request for them to look into a $700 Tock charge.
They also made it clear that whatever is written on the statement as the category (e.g. "Restaurants - restaurants") has nothing to do with what it is coded as in the backend. Makes no sense to me, but there you have it.