Update:
I pulled out the transmission today and swapped the new clutch kit, added new guide tube, pivot pin, pivot pin clip and rubber washer. However, the issue is still there. This is incredibly disheartening to say the least. The good news (possibly?) is that I think I have identified the root issue. For anyone who has worked with these dual mass flywheels, take a look at this video and please let me know if this is normal. Note that the flywheel only has about 500 miles on it at this point.

https://photos.app.goo.gl/YzQsXpmGHkNyzcbi6

What I found is that the main flywheel section, that you bolt to the motor, seems to be fine. However, the surface that the clutch disk contacts, and that has the rotational give in either direction to make shifts feel smooth, will rock or protrude with little disturbance. It lifts away from the main flywheel base a decent amount with only a little force. It seems like this would cause the pressure plate to wobble and create the vibration that I'm feeling. Is this normal? Is this the root of my issue?

 

In the future, I would purchase OEM Porsche parts from Rennpart who is sponsor on this RL Webforum. It wouldn't surprise me if the Sach's clutch you bought from Rock Auto was misrepresented and the OEM lighter Dual Mass Flywheel is a must.
Not trying to rain on your parade of bad luck with your clutch job but your scenario is why I have my Porsche Specialist Indy do all of my work.
Too many variables to go wrong.
Good luck resolving the issue.

 

Did you replace your motor mounts with OEM parts? As Jake Raby has pointed out in other postings, semi solid mounts cause more noticeable vibration
and often can cause the knock sensor to retard timing.

 

I did, but that was about 5k miles ago. The new mounts helped tighten things up but didn't introduce any vibration.

 

I only replaced the dual mass flywheel on a late 996 model just once. I do not recall it ever had any movement in that dimension. In the rotational dimension, yes but not in the z-axis like that. That is easy to check on the new flywheel if you buy another one ($1,000 for the non-Porsche one)

 

Update: I replaced my flywheel (again) and the vibration issue is solved. Based on the play I was seeing in the dual mass function of the flywheel, something internal was defective. rockauto honored the warranty and refunded me after I returned the defective flywheel.