Until recently I owned an LT1000 and used it for about 16 years. I've always had good service from the belts I ordered from Sears parts, but not so much with the parts I ordered from Ebay or Amazon. These belts should be Kevlar reinforced or they won't last long. The tip off is that a Kevlar belt will be grey or tan in color instead of black. Some of the vendors on Amazon or Ebay will sell you approximate sizes instead of exact matches and you have to watch for belt composition. Sometimes the picture looks right, but what you receive is different.
Since you bought it from a yard products business, I'd hope they sold you an OEM belt. After all, if they install it for a customer they have to stand by it. I do know that there's two ways to install it and only the right way will work! Been there!
Compare the diagrams to the actual install just to make sure you have it over the pulleys and through the guides per the diagram. If it's slipping it's loose or one of the guides is dragging on the belt instead of letting it pass through without restriction. You should have noticeable pressure when you engage it. If you do and it still slips, suspect something dragging against the belt when it's engaged or it's outside of a guide instead of running through it. There are some loop guides in the path. If the belt passes outside of the loop it will drag instead of running freely.
