Does the rear PTO engage without and problems? Certainly sounds like a gremlin in there. For devices like these and with some high hours I would be suspicious of the actual clutch assembly though that does not really explain why the rear PTO would be of any help.
Might the mid PTO be slipping and the rear PTO slow down the connection just enough to make enough static friction to actually engage the clutch on the PTO.
Honestly, I am grasping as straws, but these are the first two ideas that com to mind.
Perhaps there is some wiring issue deep in the tractor's bowels.
Might have to take it to a dealer to figure this one out.
A few years ago, my 2305 started to lose hydraulic fluid for no particular reason. I checked up and down and NOTHING seemed out of place. Took it to the dealer and they found that my mid PTO shaft had gotten engaged while I was bush hogging. The result was a ring of grasses wound itself around the mid PTO shaft. It completely abraded the gasket but took its shape and with grass, dirt, and a little hydro fluid, it made a not-half-bad seal itself. I would not have found it as it was so perfectly would into place. Deere gave it back to me and I was amazed at how perfectly it fit the original gasket.
The moral: Sometimes you just have to take the darn thing in
Hope it gets better for you
SI2305
JD 2305
200CX, LX4, 60" Grader blade, 60" LandPride finish mower that replaced our old lawn mower, middlebuster, home made grass rake for long field grass collection, and now a specialized trailer to move heavy logs