My hydro lifting thoughts here... and again just thoughts without being able to physically inspect the unit.
By operating with the system HOT... Do you mean the oil is within the accepted heat range for optimum operating temperature or is the oil truly hot and above the heat range?
If the pump is truly worn out then none of the rest of the pump functions would work properly such as forward/reverse. These are working as should unless you've tried forward/reverse when the engine is idling and the tractor doesn't move like it should either.
Check the charge pump and implement relief pressurees when they are cold and then at the HOT temperature that you mentioned. Checking when cold will tend to give a false reading.
I'm right now leaning towards a weak/worn out charge relief spring or worn out implement relief spring. If the springs have already been shimmed up to the max then a new spring is more than likely necessary.
Changing pistons or kits can be the cause only again... everything will show up being affected also.
Charge pump could also be getting weak. That is where checking the pressure when the oil is at operating temperature is important. You will get a more eaccurate reading.
I'd personally leave the low hour 1250 alone and if you don't want it then sell it. Someone out there will definintely be happy to purchase it and the tractor could go via the Cub Cadet Transportation Network route.
A little F.Y.I. for All. In 2014 the 15 Series is scheduled to cease production as a factory made unit. It will and is even now being replaced with a 20 Series pump. What this means is that after the 15 Series line shuts down then no new units will be made however parts will still be available. Please don't ask me if the new series will be a direct bolt in. I haven't seen them yet so you will have to write the company and ask them.
I hope the above thoughts gives some helpful input.