I've done this a few times with my home DAT deck (Sony DTC-670) by adjusting the tape guides with a small screwdriver white the tape was rolling. I listened the tape and adjusted the guides to get rid of the "buzzsaw"-sound. Once it seemed fine I just cloned the tape!
It IS a pain in the ass and takes a lot of patience but if the tape is somethiing really important it is probably the only way. Of course you'll also lose the aligment on the deck but my deck was messed up already so that wasn't a big deal...