What do you consider a decent price? A problematic 388 doesnt have much value, and if the tape side is non functional, you are left with a very large heavy 8 channel mixer
As far as the reel spinning too quickly, the reel tables are direct drive while the capstan is belt driven, so I do not think it sounds like a belt issue.
If a tape is not loaded, and you hold up the tension arms and press play, the takeup reel WILL spin very fast....its the capstan that regulates the speed of the tape, and the takeup reel motor just keep a constant tension on the takeup side. if there is no tape loaded, the takeup servo/motor is trying to tension up a non-extent tape and will run like blazes. If there is a tape properly loaded and it runs fast, then check to make sure the capstan roller is pulling in against the capstan shaft. It it is not, the takeup reel motor may still pull the tape at a fast speed, and the problem lies with the pinch roller solenoid. If the tape is loaded properly, the capstan and roller are engaged, and the thing STILL runs fast, then .....I'm not sure, but there probably is an internal speed adjustment for the tape speed. It should not have so much range that the tape is screaming thru the transport however.....
Oh yeah, make sure the varispeed is set to internal and is shut OFF.
Check it out and let us know.