Yes, the belts do stretch and they develop a glaze over time, both contribute to slipping under load. I had a similar problem with my Craftsman LT1000 with hydrostatic transmission and where reverse was weak. I used a mighty vac to remove suck all of the oil out of the transaxle and replace it with new. I did this twice with a short run time between “flushing” the old oil looked pretty dirty. It is much better now and has been a couple years.