So I updated the firmware on my ND-2510A to the latest available, 2.18,
and updated my burning program (Nero) to the latest edition, 7 Premium.
Windows still wasn't recognizing blank DVD+R9 media, but Nero was, so
I decided to go ahead with it anyway. The whole burn took 38 minutes
at 2.4X and the total time was over an hour including verification.
Simply put, "fast" dual layer media doesn't even exist yet.

And now the DVD works! (I tested it with Ghost in the Shell: Stand
Alone Complex Vol. 1) It's correctly recognized by Windows and plays
just fine in media players. It's kind of funny how it goes from a
totally unrecognized blank to this, but whatever. I'm just glad it
worked. Soon I'll test it in a set-top DVD player.