Did you buy it new?
I bought my JD 5525 new in 2005 it has under 2000 hrs. I never had any issues with it and no major service. It has never been back to the JD dealer since buying for service. Thankfully. My “run-ins” with the service manager were not pleasant. Others have said the same.
My local JD was bought up as others by a “company”.My farmer neighbors have said the new ownership sucks compared to when it was family owned.
Replacing the clutch and usually the plate should have no bearing on the issues you are having. If the clutch was installed incorrectly and you are loosing “power” the RPMs would go up without an increase in speed/power.
The cooling system is pretty much the same since water cooled engines were first made. Either the water circulates properly or it doesn’t. Pretty easy to diagnose. Assuming it is a “generic” cooling system there are only 2 replaceable parts that can fail, the thermostat and the water pump. Thermostats can and do fail, stay closed or only open partially. I don’t know the tractor but replacing a thermostat is usually a very easy DIY unless it is buried under a lot of stuff that has to be removed to get to it.
When I have suspected a bad thermostat I just take it out reconnect everything and run it. If it runs normal Bob’s your uncle install a new one. They should be pretty inexpensive but JD can and does rape,rob and pillage with these sort of parts.
Keep in mind that depending on ambient temps it may run on the cool side of things because there is no thermostat opening and or closing to maintain designed running temps. But IMO and experience there is no harm in using it until the thermo is replaced. Unless this tractor has a computer controlled fuel regulated system. Which meters fuel delivery based on engine temps sent by various sensors.
Failed or failing water kind of usual on a tractor can usually be diagnosed by running until the temp gauge hits normal and or higher. Put on a pair of gloves and squeeze the hoses, return and supply from the radiator. They should be pressurized you should be able to feel water circulating, in other words check for a “pulse”.
The only other thing is a clogged radiator and or a clog in the water ports in the engine. But this was just serviced and I would like think after servicing they would have checked things out for proper function before giving it back.
As to the PTO shaft, is this a belly mower or 3 pt hitch? Either way I don’t see how this would have an effect on what you are describing.
Your tractor and mine have basically the same type of hydraulic system which “runs” just about everything, transmission, bucket, 3 pt hitch, power steering, etc.
There is a filter (pricey) that has to be replaced from time to time. My tractor will drops a lot in performance and runs hotter when it needs changing. With my tractor it needs to be changed a lot sooner then the service manual states. With 1000 hours I would change it as a matter of course. With a new tractor this is usually changed at around 300 hours. The service manual will tell you.
This is an easy DIY also. Not much different than changing an oil filter on a car. You will need to buy additional hydraulic oil. I don’t buy it from JD their price is out outrageous compare to the same thing that can be bought at Tractor Supply.
This link shows where the filter is on your tractor. About 3/4 of the way down the page.
http://manuals.deere.com/cceomview/OMM139226_A9/Output/OMM139226_A910.html
The lack of power maybe fuel related. Failing injector pump? But the tell tail is usually “white smoke” from the exhaust from time to time and the “song/tune” of the engine changes. Possibly failing injectors.
Every piece of power equipment has its own “song”. When it starts to sing out of key something is wrong. Different “notes” can mean different things. Help in diagnosing.
MY JD has run like a champ for years, never had fuel problems or any major issues. I run some big equipment with it, bale a lot of hay, use the FEL to its full capacity if not over. Which is why it has a great re-sale value. Especially from a horse operation. Farmers know they are lightly used compared to what they do with them.