Check the width of the belt. There is a minimum specification. They narrow due to wear.
You could try watching the primary and secondary while under power, but this requires removing the plastic housing and raising the bed. Caution is needed when doing so, but it can give you a visual clue as to what is happening. Could try this first on jack stands to verify complete belt travel. If complete travel is achieved on the jack stands (no load) proceed to the flat land, but use extreme caution. Very unlikely its an internal transmission problem judging by your comments.
Curious how are you judging engine runs fine if it can't accelerate? Low power will prevent it from accelerating. Diesels get there power by controlling fuel flow and behave differently than gas engines. Poor fuel flow will restrict hp and prevent it from delivering the desired performance. Typically a miss or other gas like symptoms are not noticed, just a loss of power.
Wish you success in fixing your Gator.
2012 JD855D OPS Black Poly Roof, Deluxe Cargo Box, Front and Rear Protection, Power Lift, Front Hood Rack, Rear Screen (homemade), 800 Watt Inverter, 2500lb Winch installed in cargo bed, Front and Rear LED auxiliary lighting (4" square 27 watt), Front and Rear CV Guards, Koplin Side Mirrors