Hi DBellaa, BillTxn, All,
Thanks again for the help. No more of the messages for a week now after deleting all HP Diagnostics files from the C Drive. I had previously changed the settings of both printers per the suggestions in this thread (which didn't fully solve the issue).
If the messages resume after the next Epson software update, I'll retire the HP printer and purge the computer of everything HP. The cartridges are too expensive anyway.