So how long is your driveline, is it one piece from the trans, all the way to the rear axle? It should be two, one from the trans to the carrier, and then another one from the carrier to the rear. It shouldn't be just one.
It is three universals. A yoke at transmission, and another at differential. Two sections of shaft. Front is tube, I'd guess 4" diameter, approximately 4' long. the carrier bearing is at rear end of this. Rear section is splined, about 3' long. That is next step, to jack it up & run at highway speed. At low speed there is almost no run out. Shaft is not balanced, but at 2000 RPM I feel it'd take a lot of out of balance to cause this much shake.
I went to the fire house yesterday. The truck most similar in size is the rescue truck. It has the same configuration but smaller diameter & U joints. Each segment of the shaft is phased the same each end, like mine was before I turned it at the spline 90 degrees.
Everything I find on the internet shows a two universal driveshaft. Middle section is always phased the same. Yokes at each end are the same angle. Nobody addresses what it should be for a three universal shaft.
Oscillation is greater in sharply angled joints. None of the three in my shaft have more than a few degrees of angle. The middle has none. My logic has been that the middle joint is not contributing oscillation. Like a straight two U joint shaft, as in a pickup, both ends of the shaft should be phased the same.
I rode as a passenger in my son's GMC 2500 towing a 25' long deck over trailer empty yesterday. I was thinking this rides similar to my bigger truck empty. I'm going to try letting some pressure out of the tires.