Your 755 is doing exactly like one of the two 750's that I had years ago. The fix for mine turned out to be adding an extra solenoid to it. I believe that JD may actually offer this as a kit. There have been a couple threads about this in the past and you might try searching for them. I think they might have been in the Parts/Repairs forum. The problem with mine was that over time all of the connection points get some corrosion in them, which adds resistance to the circuit. This extra resistance creates small voltage drops, and also limits the current getting to the solenoid. Not only that, the wiring in the ignition switch/starter/soleniod/ circuit is slightly undersized in places which also creates more slight voltage drops as well. All these drops are sufficient enough (when added up to together because they are all in series) to cause the starter to work erractically at times. Mine got to where I had to turn on the key to start, then hit the starter with a mallet whenever I wanted to crank it. Adding the relay jumpers the 13.8v from the heavy gauge wire going to the starter motor over to the smaller wire that goes to the solenoid, but only when the key switch is turned to the start position. In essence, the relay provides a little more voltage to the solenoid so it can do it's job better. You might talk to a starter/alternator shop and see if they have any knowledge of this. If they've ever worked on any tractor starters, then they probably have seen it before. I just know that after I added the extra relay to the 750, it cranked first time everytime and never had to use the mallet again.
One other thing is have you checked to make sure your ground wire on the battery is grounded to the frame good? Could be some corrosion on that end of it too. Good luck!
