Congratulations and thanks for all of the photos. I know it takes time and getting on and off of the tractor often for such a task.
The idea of attaching 4x4s on the skids is a good one both to raise it for hooking up the 3 PH and keep it from contacting the ground. Treated wood would be best.
Most chippers that I've seen, and own, have a metal frame underneath them for them to sit on for the "keep off the ground" function.
The PTO shaft will vibrate if the shaft is not almost perfectly straight. That is another reason for the frame on most chippers - to align the tractor's shaft and the
chipper's shaft.
Try lifting the
chipper with it running (at idle or low speed) to see if the vibration amount changes depending on the amount of the angle off of horizontal. At horizontal it should calm down to nearly nothing. From the pictures it appears that it is lined up correctly so there should not be the shaking. See if the looseness can be identified.
Some chippers need an adjustment to the flywheel to keep things in alignment. The instruction manual may have the adjustment procedures. A friend of mine had a Chinese
chipper that we spent hours on trying to adjust this bolt and that one to align the darn thing. Finally got it done but it failed and was returned for other reasons.
The "Quick Hitch" frame is not the best for lifting pins that vary in width from implement to implement. Also they can be a pain if the top hook doesn't have a clear path to catch from underneath. I've owned two of them and sold them in favor of Pat's Quick Hitch arrangement. Too late now, I know. Just a comment for reference.