Thanks for the suggestion, but I already tried this with my HP Color Laserjet 2840. When I attempt to scan this way, it brings up the scanner dialogue for HP Scan, but the scan button is grayed out so I am unable to scan.
This method works fine for my Brother scanner, however, as does using the Brother scanner software. It is just HP being the lousy company that it is. I wish I had purchased a Brother or Canon color laserjet printer, then I wouldn't even be having this discussion.