Okay, progress, I think. Another thread mentioned using M851 to manually re-write the Z axis offset. Once I did that, I was able to run the Z-axis calibration without smashing the nozzle through the bed.
Also, I figured out one thing I'd been doing wrong -- the checkboxes only go down to 0.05mm if the Fine Tuning box is checked. Which I kept checking, b/c it was the only way to get the lower-left 'New Z Offset' box to become writable.
Still no idea why I couldn't get the initial Z offset value to change without resorting to manual M851, but once I did that and was able to get the Z-axis calibration to work, I *seem* to be able to print -- I have a test print running now.
One thing that stands out, though -- the nozzle has been smashing into the bed for so long, my bed is now seriously bent. But the Z-axis calibration seems to be taking care of that -- I can see the bed moving up and down in sync with the Y-axis moves. It's quite interesting to watch, although I wonder about the possible side effects of Z-axis backlash with all the up-and-down motion.
Here's a question: now that I (fingers crossed) have the Z-axis issue worked out, is the bed levelling resident in firmware? That is, if I switch to RH or S3D, will the bed leveling be retained? If I can't get the software bed leveling to work with other software, I'll be stuck with SoliPrint (ugh) for the forseeable future, because I don't see any way to physically level this bed, bent as it is, short of trying to bend the entire assembly back up.