It seems like there are two things going on.
I haven't checked the pictures but, based on your having to back off the high gear limit, I suspect that the hanger is bent inward. An easy way to check is to shift to a gear where the derailleur cage is close to vertical. Then set a straight edge, ie. a broomstick, against the rear wheel as a reference, and see if the cage is parallel to it when you look from the back.
The other issue may be a new chain on a worn cassette. This tends to cause the skipping under load on smaller sprockets. It's possible that the prior owner replaced the chain, but not the cassette.
For the moment, I'd get the hanger alignment right, then adjust everything and hope for the best.
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