OK, so this is what I found today. First I did the transmission hill test. I wasn't sure what level of slope you meant to use so I did a few different slopes. First I did it onthe back yard hill that is giving me problems trying to come up. First test was on the right side, where the tractor is sitting if you zoom in. I let off the brake and the tractor very slowly rolled all the way down the hill to the shed. I did not have to push it to get it started. But it was pretty slow, maybe 3 mph that I just slowly walked beside it. Next I did the left side of the hill next to the tree. It doesn't really show in the picture but that side is much steeper. I expected it would roll much faster, but it just rolled down at the same slow speed. Then I went to the side yard, a little less steep. This time I had to push it to get it moving. It went about 10 feet and stopped. Then I went to the driveway which has just a very slight slope (yes, I know the driveway needs powerwashed, it's on my list). I could not get it to move at all in the driveway. What does this tell you about the condition of the transmission?
Next I drove it up the steeper left side of the back hill to check for a squeal. I was able to drive up 3 times without any problems. It didn't slip at all. At this point I should mention that I always cut the back hill last. So I cut all the other grass then tried going up the back hill and now it got only half way up the left side. There was a squeal but I'm pretty sure it was the belt squealing. I tried looking underneath to see if the transmission pulley was turning when it squealed, but couldn't see. I did notice, looking through the slot for the gear shift that when it squealed, the fan on top of the transmission slowed down. The belt turns the fan right? so if the belt is slipping, the fan will be slower? So I deduced from that, that while I'm cutting the front yard, the belt is getting hot and it only slips when it gets hot (and expands?)
So next I pulled it in the garage to check underneath and I may have found the problem or at least part of the problem. First a question - The first thing I noticed is there appears to be virtually no clearance between the belt and the guide (circled in yellow). It looks like the belt is slightly rubbing the guide. Notice the slight fraying of the outer edge of the belt. Is that lack of clearance normal? How can I fix that? Next I removed the idler pulleys and discovered that the flat pulley spins (not quite as well as I would expect), but the V pulley turns freely but does not spin. I don't know how I missed this when I replaced the belt...I thought sure that I checked the pulleys then. So I'm going to order new pulleys. I checked the numbers on the pulleys to see if maybe they were the wrong pulleys which might explain the lack of clearance with the belt guide, but both pulleys have the same number GX20153? The numbers on the parts diagram are GX20287 and GX20286. Do you think the drag created by the pulleys going bad is enough to cause the belt slipping problem?
Also, there is an adjusting nut behind the spring on the transmission linkage circled in blue. How would I know if this nut might need adjusted one way ot the other? Could it have anything to do with my issue?