Hello Richard,
If the LoL causes the tape to squeal in the transport, let me remind you of a procedure that works on open reel tapes (which is sort of what your cassette tape is after you lift the pressure pad): Stick-slip ("Stiction") is a function of the tape speed -- the slower the tape goes, the more squeal there will be, and vice versa. So if you have one of the cassette players that goes double speed (3.75 in/s), there is a chance that the tape will run without squealing. Then use an open-reel machine or a computer to bring it back to speed and pitch.
Or maybe you do this already?