Condition of rubber drive surfaces and cleanliness of the surfaces driven by them; proper assembly and condition of the drive linkage, overall; condition/packing of the tape being driven; etc. Operation with the face off should tell you where the drive slipping, if any, is occurring. I believe you have enough information to sort this one out now. Just carefully familiarize yourself with how it all works, and spend some quiet time. Come back when you have substantive information to report.
Do not go stretching or shortening springs, or filing on anything, or anything non-OEM. Just report back when you have something definitive. Relax and enjoy the learning process.
You can fake the machine into believing that it has a tape in it, by pushing up, and holding, the cassette retainer, in the top middle of the transport. Then when you hit FF you can put resistance on the take-up reel and see if it slips or provides nice consistent torque. Put it in REW and do the same, but you will have to rock the take-up reel back an forth to fake tape motion, or the deck will stop in a couple of seconds.
Enjoy,
Rich P