not op, but from my experience overlined ts are a thing from a bygone era I'm afraid. my parents sometimes do it, but I don't know anybody under 30 who would write it this way. on the other hand I do sometimes see it written like a print т.

what you said about mixing up cursives is really interesting! I think the only case where I mix up mine is when writing a p instead of an р (the russian version typically doesn't have a loop).