you'll need to take the right side cover off. set the shifter in neutral, look at the outside shifter rod as both ends the rod bolts should be facing downward, correct this first,then remove the outside rod(10 mm.) from the shifter, the rod bolt when the shifter and transmission are in neutral, should fall into the shifter hole, but it sounds as if you need to shorten the shifter rod for proper reverse engagement. loosen the locknut on shifter rod and adjust as necessary,you may need some penetrating oil on the threads.
still be a good idea to take the shifter off and clean the internals. polaris wants a refill with there synthetic but whatever 0w or 5w you have laying around will work and just add enough to cover the shifting arms.
if you still decide to change your belt ,be sure to air blow or clean the front clutch.