It may not be capstan speed, rather may be pinch roller related.
When I have had this happen it was because the pinch roller was not fully engaging with the capstan shfat, thus the tension on the takeup reel side was pulling the tape thru at high speed. If you have not used the machine in some time the solenoid that moves the pinch roller may have gummed up lubricant or be otherwise sticking. Try pushing the pinch roller over when you hit "play" and see if this solves the problem.
If this is the problem, some disassembly and clean/ relube of the pinch roller mechanisim would probably get you going.