I have a 175 hydro that puts out 12+ volts to the battery when I check with a meter at times and at other times the PTO quits and the battery output to the battery is below 8 volts. I have been through 2 batteries in the past year.
I kno nothing about John Deere hydro i'm a motor bike wiz, And your problem sounds like a regulator rectifer you should be getting +14 volts DC across the battery when the engine is running,(same value for Bikes,cars and vans)
Comming off the alternator you usually get
above 70 volts AC.
Hope this helps