Here it is Friday and all of the logistical problems have been cured, the parts I ordered were correct, and my 580 now has a 30" mechanical tiller attached. Thank you all for the support.
With very few problems the hardware was easily attached to the 580 chassis. However, there are a few issues you won't find in the book, the first one being the bushing size for the front of the tiller chassis latches. The bushings used to mount up front using the latches are too big. They are too large in diameter and the result is you'll get the tiller chassis in place under the tractor, but you won't be able to seat the chassis or close the latches. I pulled the chassis out, took the bushings off of the tractor frame, then ground the bushings reducing the diameter by .062 / 1/16". Problem solved.
The next issue to be aware of is the insertion of the lift link running from the hydraulic lift cylinder to the rear yoke mounted inside the chassis. There is only one way to thread this link back to the yoke through the chassis. That method is to lay under the tractor and slide the rod through the chassis from front to back. It would also be helpful to have a second set of hands that can grab the link when it gets back to the yoke or it will fall out and you'll have to start over. (Thanks to my wife.)
I had given thought to buying the Sears/Agri-fab tow behind tiller, or a DR tiller, etc.. After using the tiller I am very, very glad I did NOT buy a tiller of that type. especially knowing that the tine shaft uses shear pins. I had read a lot about shear pin issues with these tillers, and constant replacement would have driven me out of my mind, especially tilling the rocky hard soil I was tilling.
The JD 30" tiller is a beast. The tiller was set to a 4" depth for the first pass and chewed through the hard soil, and lifted not just rocks, but large rocks and small boulders out of the soil with little or no effort other than an occasional screech of the drive belt if the tines hit a very large boulder. The tiller was stopped once, and only once, when a 6" rock became lodged between an outside tine and the tiller housing. I banged it out with another rock and never stopped after that.
My only other surprise was the force generated by the tiller. For those who don't own or haven't used a tiller of this type I'll note that the tiller is offset to the right behind the tractor. This is done so that tilling from right to left, or in a counter clockwise circle as I was, the tractor tire marks are covered by freshly tilled soil. If you look at the photos below you'll see that l live on a fairly steep hill, steepest on the left side at the top.
My first pass was from bottom to top ending up with the first downward pass being from the steepest point on the hill. I did NOT expect the tiller to take over and shoot me down the hill at a very high speed, even with the brakes full on. I almost panicked. The reaction was sudden and uncontrolled and I advise extreme caution to all if you are in a position where down hill tilling will be involved.
At any rate, I changed my rotation to clockwise, climbing the steepest side of the hill and down the not so steep side. Again, I'm very pleased with my purchase, don't have to worry about shear pins, and have an attachment that has cured a problem, and that will last for many years to come.
Hope this helps.