Originally Posted by UncleWill
I know this is opening up a whole can of worms, but having tried digital, in my personal opinion open reel tape captures the human voice much nicer. Granted that all the sound clips are edited on a computer in lossless digital, I still think its worth having to put up a little extra effort for our listeners.
Can of worms - maybe. There are advantages to analog tape, but these days they really do not matter - digital recording can now do very well. You might consider trying again using your existing Mic and preamp (likely you can run it right into a laptop)
Unfortunately I can not answer your original questions. I have no knowledge of your specific machine, or repair places in your area.
I would say that wobbly reels is not a common problem on a well made machine. Inconsistent take up speed can be a problem, but the reel should not wobble side to side.
I guess the first thing you need to determine is it the reel that moves side to side, or, is the reel shaft wobbling. Take off the reel, does the shaft move at all (except round and round)? If the shaft wobbles, you might have to replace a few bearings/bushings which would be cheap if they were still available. If the shaft is solid, you might just have a bent reel (which sounds like all it may be).
You might be better off just buying another used tape player that is known to work well. It might be cheaper than fixing what you have. Again I don't know your machine - there might be a common problem that can easily be fixed. Did you google your machine?
I don't know about what they are doing at college these days, but I'd suggest you convert to digital recording - then processing it if needed to simulate your reel to reel. This is a skill you can carry forward. If you already have a mic and preamp you like, and a computer, you are (nearly) ready to go!