I’m not that familiar with lg drives (don’t have one), but since no one else has answered yet , maybe I can point you in the right direction till someone does. What you are referring to with the firmware change is called cross flashing. Basically, only a handful of companies make drives, but there are many more brands, that just buy drives and slap their name on it (my micro advantage is an aopen and has been crossed flashed to an aopen, my mad dog is an nec but has not been crossed flashed (I like the mad dog firmware better), I have a plextor that is a benq (haven’t gotten around to cross flashing it). Often the firmware is special, sometimes it is the same except for a small part that tells what drive it is, sometimes it is completely different firmware (but the drive is identical down to the last screw, but the label and firmware is different). Your hp is an lg (lg made them and sold them to hp). They put hp firmware on it though as it is a hp (and the hp firmware may be better or worse, and may have certain features disabled as you have found out). Cross flashing means you flash it to lg firmware. For all intents and purposes, it is now an lg drive and will perform and have the capabilities of one.
Cross flashing has risk. If your computer is very stable and has a battery backup, the risk is very minimal. the risk is the same as updating firmware, if power dies, or something crashes during the flash, the drive may be dead (some can be recovered, not sure about lg’s). If you are flashing official firmware, a bad flash is usually covered by warranty, but with cross flashing, the fact that you are cross flashing voids your warranty). You usually have to either use modified firmware (self installing from windows), or use a modified firmware (not self installing), and use another program to flash the firmware to the drive. as I understand it, you need to get modified firmware and use a special program to flash it (just searched, not familiar with lgs so please confirm what you are doing).
In other words, surf the lg forum a little, and find what is the best firmware for the LG GSA-H20L, find the right cross flashing program, and use it to install that firmware.
I found this old thread, maybe it will help. As it is old, I would defanatlly check to see if their is a newer better (maybe safer) way to do it.
Hopefully that will point you in the right direction.
Almost forgot, here is the lg forum in case you havent found it (your drive is an lg with hp firmware, so this is where to find info, check out the stickies and or search limiting to this forum).