ok, I figured it out. I feel stupid!
It turns out that the tire on the rear was [likely] original and was so badly worn out that it was down to the casing and threads in some spots. My theory is that under load, the tire was collapsing under my weight. That would explain why I couldn't feel anything when the bike was in the stand or in my hands.
A few weeks ago, while leaving work, the tire gave up on me and I literlly had a blow out. A loud pop and my tire basically disintegrated.
When i got it home, I saw how bad the tire was. I probably just never noticed it because the fender was always covering it.
Anyway, I ordered some new Kendas and got them on the bike a few days ago. Hey, no more wobbling!