Progress. First a learning: It was suggested earlier in this thread that I engage the PTO at an rpm level above idle. Per the rpm gauge on the MX, idle is at 800 rpms. As I was fueling the tractor today and edging it back and forth at idle rpms to get it closer to the fuel tank, I changed the HST pedal pretty quickly from reverse to forward and the tractor shut down. I hadn't noticed it before but obviously this tractor is sensitive to sudden and different hydraulic loads. I greased the new PTO shaft and joints and put it on the mower. I have more than 15" overlap with this new shaft. I removed the mower from the tractor, checked everything, hooked it back up making sure the 3PH connections were like they should be. Then I took the tractor and mower outside to a clear level spot, lowered the mower to the ground (another suggestion earlier in this thread), and engaged the PTO with the engine at idle. It worked. Shook a good bit but less than before. I shut everything down, cranked back up and engaged the PTO again. This time the mower shook a lot and the tractor shut off. So I started over but this time I inched the rpms up to 900. There was definitely a different tone from the engine. Engaged the PTO again and it worked fine, with actually less shaking. I shut everything down and tried the sequence again, this time at 1,000 rpms. The mower got started okay but it seemed to shake a little more, didn't start up as smoothly, as engaging at 900 rpms. So I did some mowing and during the course of the mowing shut down the mower and restarted probably 7-8 times, each time with the mower on the ground on a clear level spot, and each time at 900 rpms. The engagement worked each time, and usually shook some but was more or less like I have been used to with having used rotary mowers for over 30 years. So the changes were a new and longer PTO shaft with very good overlap, starting with the mower on the ground to dampen the shaking some, and engaging the PTO at 900 rpms versus 800. My conclusion is that maybe no single one of the changes would have solved the problem but all contributed and the MX5800 and mower are working together. And varying the rpms just from 800 to 900 seems to have helped a lot. Just a 12.5% change. And it was interesting that moving up to 1,000 rpms didn't work as well as 900 rpms. I still plan on taking off the blades to make sure they aren't bent, but I think I am good to go now in the sense that I know that the tractor and mower can work well together. And the mower just hums along at the full 540 PTO rpms, which is 2,650 engine rpms for the tractor.
Thanks to everyone who contributed thoughts. As I learn more I will report back.