I can't speak to the compatibility of specific printers, as we don't have an HP1000 printer to test on - but we do have other HP printers which are fine.

If you choose multiple customers to print statements for, and select the HP1000 printer driver, and preview the statements rather than print, do you get one statement or 3? How about sending to the fax queue? This can help narrow down if the issue is printer driver-related, or hardware/print job-related.

Specifically, if the fax queue is complete, the print statements function is working (as you found when choosing a different printer). If print preview works with the HP1000 printer, then the print job being sent to the printer is incomplete - take a look at printer settings, time outs, etc.