The MX5050 is notorious for this kind of symptom due to switch and pitch control dirt that get into those parts. They are also due for new electrolytic capacitor changes on the power and control boards. The 10V orange caps are noted for shorting. When I see a 10V cap due to my experience with them they are replaced with 16V good cap on sight.
There is a foam that rots and can affect the circuit on that board as well. It should be removed and cleaned well.
On the Teac, the speed can slow over the years which is why I have had made a special modified pulley to get the speed up. Even after oiling the capstan shaft with AMS Synthetic oil and new belt and motor oiling the speed was still substandard like at 2840Hz for a 3K\Hz test tape. No matter what I did to get the speed up did not work until I had the pulley on the motor made that put the deck back up at 3007Hz. The pinch roller pressure was correct and there were no brakes dragging- I kind of know about this stuff having worked at Teac Factory Service 8 hours a day in the 80's.
Unlike other shops, my units go out with specs or better when I release them. All you need to do is the same as I do and I do not keep it a secret.
The pulley that helps is a $42 part and it is 10/1000" larger than the original one at the peak of the crown. If you have other questions I do answer them through E mail.