Hey all,
So - here's some resolution of sorts to this issue.
Thank you to everyone for all their advice. I tried a dial out indicator and that didn't help at all so, sparked by the idea of servicing the turntable, I contacted VPI, who gave me the contact info of their "dealer" in my area, whom I then contacted.
He and I talked and he gave me a detailed primer on what to do before I brought it in - including checking the spindle and the bearing well for all sorts of contamination. Which indeed I did. Yes, there were a few cotton fibers down in the well, and I cleaned all the old oil and debris out (old by about a year and a half or so) and dropped 2-3 drops of 10W-40 oil into the well. I kept the same bearing, though, for now.
Then, I carefully placed the platter back onto the spindle, seated it, then adjusted those three pesky leveling screws until each was equal in terms of tension. I then placed a GeoDisc onto the platter to check my cartridge. All of a sudden there was a palpable "thwock" and the platter dropped another half-inch or so onto the spindle -- thus seating itself firmly where it should have been all this time.
Lo and behold the platter spun level. Now, was this because I inadvertently leveled off all three screws? Had the platter not been properly seated on the spindle before? Had the spindle not been seated in the well? Don't know, But massive platter is as level as it's ever been.
And now I have a new audio destination: Defiance Audio - about 20 minutes away from me. A maker of speakers and an ersatz VPI dealer, Adam at Defiance talked me through troubleshooting the VPI and I'm looking forward to visiting his workshop and hearing his speakers.
And thank you to all here on this forum.