Well what do you know, sometimes overthinking is not the solution. After The struggles with my previous approach, I decided to rethink what I was doing. Taking apart the cassette player and basically rebuilding it did not make a lot of sense. So I figured out a way to instead mount the tape inside the cassette player. And what do you know, that was probably the easiest solution I could have done in the first place. I modeled some tiny cassettes that can hold a very short strip of tape. 

I put some bits and bops in place so you can have a variable length of tape. The only downside with this approach is that you have to have a somewhat long initial length in order to get it working which was not the case in my previous approach. However. having it working is better than...not having it working. So. The next step is to hook up some micro controller and change the speed of the motor.