Well, it's been along, long time, but I thought I'd report back that the problem is solved, but I have no idea why.
I used the Murray several times this year, racking up about 10 hours over the warm months, with no change. Still shaking. A few weeks back, I was doing my last cut of the year. Everything was already brown, and I was mostly just smoothing down the top of the grass. There were a few drifts of leaves in the back yard that I didn't feel like raking, so I drove over them with the mower. On the second pile (pretty deep, maybe 8-10"), the mower bogged, shook even harder than normal, there was a bump/bang from the deck, and -- poof -- the shake disappeared.
I got off and under to see if I could see anything obviously changed, but, whatever it was, it was invisible to me. Cranked back up and ran it for another half hour or so. Smooth as silk.
:confused3: