It's been my experience that commonly the belts and pinch rollers mainly wear or gum up causing mostly a slow down due to a consequence of slipping.
(Obviously you've tried a different tape to rule out the obvious)
A quick check by eye is looking at the rollers which should be a flat black, if shiny it's an instant indication of being worn out.
Both belts and rollers can be fiddly but you can replace them easily enough yourself after of course giving the mechanism a good clean, being a common generic problem YouTube has various tutorials to help you.
The speeding up can be more involving problem to repair but is well covered on the likes of the "tapeheads" website and if not wanting to repair by yourself then is possible by someone else that deals with them who can usually be found online.
It's always best to get it looked at first in view of cost to see if it's financially viable to repair or cheaper to just get something else.
All that said it's inexpensive to replace the most common issue of the belts and rollers yourself which might be the cause.
As far as a new deck comes in right now it's a good time in view of their market value being much lower for the lion share (I'm not talking rarities or collectables) of decks.
ebay using caution and PayPal is as good as any a place to start, recommendations should come from others but theres usually many a Yamaha in the KX range that offer good quality.
My last deck was a KX330 and lasted yrs until disappearing into the loft.
(There's one now there for 130 fully tested as working and serviced)
It reviewed well in its day and if I remember review as one of the best 2 head machines in its range.
I remember it was as good a player my 3- head aiwa at the time.