Ed, If you have the JD Technical Manual #TM113019, or a CD on the Z445 unit. If not, you need to get one. The paper book is about $100.00 and the CD version is about $45.00. One should never own any expensive equipment such as a lawn tractor without having the technical manual on how one can makes repairs.
If you have the technical manual, there is a section on how to adjust the "governor setting" and that is the first thing you should do here... get the governor setting so the engine doesn't "pulse" or one might call it..."surging".
I would bet the governor is out of it's normal setting and causing all the problem you have listed. However, making the setting on the governor is very tricky and should be done with some experience on this, if you get it all wrong it will cause the engine RPMs to go higher than the 3500 rpm rate and blow the engine.
Of course if you send it to a JD dealer, they will spend couple days... mostly looking at the tractor and scratching their head trying to figure out what they should. In the mean time they can figure how much you need to pay for all this, which may be up to $200.00 or more.