It's peculiar that you've had problems with the LiteOn burner, as that model number is identical to the one I have installed in my computer. I've thrown dozens of discs in the past; all burnt and verified brilliantly. IMO (and though I've only worked with a few drives) this LiteOn has been the best drive I've had.
From what I've read, all of those are good choices. Based on what I've read, you may be throttled with firmware issues, especially with the ASUS who leapt on the DVD writer bandwagon late into the game. Although all of them have their quirks (some drives will work with some discs better than others) I think LG might be your best bet, because they've introduced a new M-Disc technology which could be something
That, and you can pick up LG burners (especially if OEM) quite cheaply
That, and LG equipment tends to be quite good - if you exclude their mobile department :Z