Folks, reporting back here with more info on this issue. Your opinions are much appreciated.

I disconnected the t-mount as Nate suggested, and there was no change. I then went for a drive and obverved some facts:

#1: When I bleed the clutch, it will work fine for about 10 minutes. Then the pedal will get soft, fluid in the master cyclinder goes down, but every system is bone dry (brake pedal stays firm). This leads me to believe the slave is leaking into the transmisson.

#2: the harsh vibration is present and unchaging regardless of motion, clutch postion, or gear selected. It ebbs and flows with RPMs.

#3: When the car is coasting, with the clutch pedal depressed, and I select gears, I observe a rattling noise coming from the transmission. I took a video of this sound, and you can hear it very clearly about 17 seconds in: https://youtube.com/shorts/S0jTuFyUV14

Here's what I'm thinking is happening. Brake fluid has seeped into the clutch, damaging it and throwing everything out of balance.
In regards to that sound, hopefully it's a pilot or throwout bearing? If not, something internal to the transmission, which wouldn't be connected to the other issue. This issue is concerning because it only happens when gears are selected.

What do you all think? This is obviosuly a big setback so I'm trying not to be bummed about the whole thing.