Most likely it is the deck belt. As the belt V wears, it gets closer to the outer diameter of the belt so it's deeper in the pulleys sort of making the belt longer.. and MTD belts aren't the greatest for longevity IMO.
And being a manual PTO, you could, WITH THE ENGINE TURNED OFF, Engage the PTO and check the belt tension.
I Have an LTX1040 which uses the same belt i believe and similar PTO system and slow engagement is usually a symptom i get when i need to change the belt.