New carriages, with the hardware-free belt catches were installed. Along with these carriages, there was a design change to suspend pulley holders from the top of the printer by two screws. These screws can be used to adjust tension, without altering the attachment of the printer top to the frame.
These changes seem to have been an improvement. I can still see criss-cross pattern on the bed probe, but barely.
As near as I can estimate, the problem has been reduced by a factor of 4-5 in the re-build. The above data came from the standard auto bed-leveling probe. I used this data for initial calibration, but then returned to my more-detailed random bed probe to refine calibration.