Log đȘ”Welp... the ol' 3D printer finally got diagnosed. Turns out the Z-axis problems were because my Y-axis eccentric nuts got all loose and made the print bed tilty along the X-axis. So all that quizzical re-leveling effort was focused on the thumbwheels, which was already past the true source of the problem.
With the nuts tighter, that also made my infuriating probe errors disappear.