You need to do some closer inspecting while changing those two pulleys.
I try to replace that plastic V-groove pulley with a metal type if readily available at about same price.
You indicated previously that you seen the fan on the transmission pulley getting slower, which is a sign of belt slippage.
While you are replacing those two zig zag pulleys, I'm not sure on yours because I never could find a IPL, but if that is the type that pulleys swivel on a spring loaded plate that is spring loaded you need to make sure the plate that the pulleys are attached to swivels freely and that the spring is attached in the correct holes at each end. I've seen those springs get hooked in the wrong hole and the spring would not be holding the pulleys tight to the belt. (it's a strong spring is why is gets hooked in the wrong place)
A hint of the two (spring and not getting a full swivel is if that rig has a clutch brake pedal the brake pedal could be pulled back further with the heel of the foot as the mower is slowing down going up a hill and the mower then goes faster. (the more tension that those two pulley place on the belt as they swivel is what makes for more belt tension)
You cannot put a wider belt on that rig due to the spacing of the belt keeper being close to the existing belt.
Also as bert says, you need to inspect the engine and transaxle pulleys and if the grooves are worn (on the sides) to where the belt is touching/running in the very bottom of the very bottom of just one pulley the belt will slip.
The most likely suspect is the smaller front pulley up by the engine. The belt will have to be removed and the pulley pulled down on the shaft and a bright ring in the very bottom of the pulley and dished out side is a hint it's worn too bad. This will not be an easy task if the engine has a electric PTO clutch.
Also you mentioned the belt gets hot. that is a sign of a slipping belt.
I think your belt keeper you inquired about is ok. It only touches the belt when the clutch/brake is depressed giving the belt slack to slip so it's not rubbing hard when the belt is snug. (and the belt slippage even when pulling or the clutch/brake depressed will be at the smaller upper front engine pulley)