I did a lot of searching and then got under the car to check it out.
The clanking noises when turning sharply were IMO unrelated to the vibration and seem to be a simple case of worn out rear subframe bushings. You can see the marks where the subframe is banging against the underside of the body. I'm ordering some subframe spacer collars off ebay, although I consider that a bandaid fix until I get replacement bushings. If my bushings are really badly ripped or rotted out I may just resell the collars and get bushings from the get go.
The vibration seems to be related to the carrier bearing. One of the previous owners stripped out a carrier bearing bolt hole. They proceeded to cut the carpet to shreds under the seats to access the tunnel, which they then cut small access holes in with a hole saw. This compromised the strength of the carrier bearing mount and has also started to split a seam on the metal next to their cut. They drilled the bolt holes out and simply slid new bolts in and tightened them down with a nut and lockwasher up top on each side. They made no effort to make sure that the pinion angle was correct after this exercise. The vibration is 95% probably the incorrect angle on the driveshaft causing an imbalance. I'm going to have to do a bit of welding work to patch the holes/split and permanently attach the nuts so you don't have to have the carpet out and 2 people to tighten the carrier bearing. Then I'm going to have to try to shim the carrier bearing until it's back at the correct angle, which according to the mechanic I talked to at Driven Concepts is a trial-and-error thing of shimming then test driving until the vibration is gone. If all of this fails I'm simply going to get a one piece driveshaft, but I'd much rather fix it with some cheap shims than with a 350 dollar driveshaft.
