I can imagine a worn bearing on one of the pulleys that would act up more in forward than reverse...or possibly a worn or missing tension spring. How old are the drive belts? While they can last many years, I'd guess 2-3 years as an average before they'd need replacement. Look for hot spots right after the belt starts smoking, hot metal can be painful or helpful to find depending... you also might check any belt tenders...once again, check for heat in that metal or burned belt residue.

IF you find one damaged belt, suck it up and buy BOTH new replacement belts from the OEM , not some aftermarket source.. install both per your manual as a matched set.
There have been all sorts of previous posts about this same subj and many have found the hard way that you prolly don't want to risk saving a few bucks in this belt repair...

I assume that when you talk "auto drive " ,you are talking about the vari-drive and not hydrostatic correct?
Vari-drives have two beveled gears (forward & reverse> that are constantly in motion on the drive shaft and are engaged by a sliding dog clutch which is controlled by the forward reverse lever.
It sounds like the forward/reverse lever is out of adjustment and is heavy towards the reverse side.
Now the only way that the trans can lock up is if the dog clutch engages both bevel gears at the same time.
Try disconnecting the shift lever and moving the linkage by hand.
You may have so much slop in the linkage that the dog clutch is not disengaging the reverse bevel gear.

I would suggest drilling a hole in the top of the transmission and adding a 1/3 quart of gear oil. This will allow the shift lever to move freely and then you need to adjust the lever so it goes into reverse and forward and neutral. Your manual should show you how. These MTD transmissions are packed with grease that looses it's effectiveness over time.