....there is a lot of added noise when the machine plays. it's weird, at first it seemed to have a strong pull in play mode, then it suddenly lost that. ffwd goes okay until about 3/4 of the tape, then it stops, and rew barely works at all. i looked, and it seems the problem is with the wheel with the red dot on it that's inside the mechanism. against this runs another wheel via direct contact with a rubber belt only around the wheel, and that seems to be slipping...
uhhhhhhhhhhh, sounds like you've got the "situation" on hands
see attached picture (I don't have any better shot

)
(If you look through a magnifying lense): The surface of That little rubber "tire/shoe" (not sure about correct technical term for it

) is (should be, that is) actually not flat but rather like a "micro-gear", and so is the "plastic hub", so the rubber "shoe" and the plastic hub should mate-lock like gears.
So when that rubber goes old and bad it gets flat and will slip. You get noise, lose FF/RW power, and may not be able to play, as the take up "reel" will not spin fast/strog enough or even stop spinning completely and you get AUTO-stop kicking in in the middle of play.
I had that situation. The only way to fix it is to find another 144 for parts or just that part that is still good and replace that rubber shoe.
Also it's a pain in the a%% to do without completely disassembling the transport block (which I don't recommend) - DON'T DO IT!!!!! - it's IS REALLY hard to put it back together as hundred of small parts will be all over the table. heh heh...
I 've managed to replace that rubber shoe by first cutting the old one with aven knife reaching it through the hole and it comes off.
Then I used long curved nose surgical clamp to slip the "new" shoe back onto the pulley.
I don't think TEAC-parts dep. still has those parts available. Or am I wrong? I may be wrong. I have no idea really.
best regards and good luck