I am trying to print 20 sets of a workbook containing 7 total sheets
containing charts. Regarding of which printer I select, all HP but different
models, or which workstation I use, with each subsequent set, the two cells
across the bottom of each page become progressively squished on top of each
other making it impossible to read.

This is not a print driver issue but an Excel issue. All printers have
updated drivers. The "squishing" occurs even in print preview. Everytime
you make a change, like increase or decrease the margin, it squishes the two
cells together by increments with each change.