Another help might be to try playing the tapes on one of the classic Nakamichi machines. I mean the ones with the dual capstans and the little pressure pad lifter. No other brand had this feature to my knowledge.
The pressure pad is a weakness of the original cassette design and amongst other things can increase "scrape flutter". The Naks push the pad out of the way and use tape tension between dual capstans to achieve tape contact on the head. Just like better reel to reel machines.
Of course the pressure pad itself may be faulty and the Nak eliminates it anyway.
Cant guarantee it would help but it might. I use such a Nak in my transfers, especially with older tapes. Sometimes I even totally remove the old pressure pad from the cassette but then it will only play on the Nak or a dual capstan machine.
The other thing that can help, along with playing on the Nak, is to rehouse the tape in a brand new quality shell. There are "C zero" shells available from duplication houses which have bare leaders sticking out, ready for you to splice your old tape's ends on. Then you can wind the tape into that cassette without ever having to dismantle the old or new housing.
You can also try and manually remove the tape pack although it can be a fiddle if you dont have steady hands. Harder if the case is welded, not screwed together. Do what's easiest for you.
If you need help there are people who do this work for a living. Richard Hess's website has more info.
Tim