It appears your HP burner is an OEM LG GWA-4162B with E152 firmware (you can double-check it on the label as shown here: http://club.cdfreaks.com/904938-post31.html ).
The only possible firmware update I have found is E223 here: http://forum.rpc1.org/dl_firmware.php?download_id=2372 . You can download and try to update, it should tell you if it’s not compatible (I hope anyway ;)).
If that still doesn’t burn your DL media, you can investigate crossflashing to a suitable LG firmware, but that doesn’t look very straightforward here (and there may be no way back, not to mention it won’t guarantee anything). A more sensible solution then would be to get a new burner with better DL support.