Speed stability could be a bent capstan, but more likely just a dirty or worn pinch roller. Could also be dirty/worn belt drive. Head alignment has nothing to do with speed stability so skip that one.
Easiest fixes first. Clean capstan and pinch roller with alcohol. Not the greatest thing long term but alcohol is fine for once in a while like this. Wash your hands first, then use a Q-tip or clean cotton cloth.
That will probably do it. If not then try the same trick with the belt. Clean all surfaces of the belt and everything it comes in contact with. While you are at it clean and oil whatever looks like it needs it.
This is 90% of the tune-up a shop would charge $100 for. The rest is belt and pinch roller replacement. You can DIY that as well. If you can find the parts.
Look closely at the heads checking for tape head wear. If you see a deep channel where the tape has worn into the heads they are worn and due for replacement. Another DIY. If worth it.
