Changing speed on DC motor with LM317?
Probably not.



Figure 1. Two cassette player motor internals. Source.

Most cassette players were intended to be run from battery supplies and had to run at constant speed with varying battery voltage. To do this they had speed controllers in the back of the motors. In Figure 1 you can see the trim pots used to set the motors' speed. Usually these are adjustable through a small hole in the back of the motor - perhaps covered with a quality control sticker.

I modified my cassette deck about thirty years ago to allow a little up-down adjustment to correct the pitch of songs that had not been recorded in concert pitch so that I could play along. I de-soldered the pot and wired an external one. I also put in a switch to go between fixed (normal) speed and variable. It worked well.