Ok, I'll reply to myself because this is incredible. Taking somebody's advice (possibly from this forum, maybe another), I switched my 1300A from my Promise controller to my motherboard controller and it instantly started recognizing my TDK +RW media. Read, write, erase... the works.
On my -RW media before, I was positive it was ruined because after writing to it and formatting it, I was told there was 0 MB total space and 0 MB free space. I was able to "erase" the disc with Nero and get 4488 MB total and 4488 MB free.
My motherboard still recognizes it as a Mode 2 drive, but at this stage, I'll take it.
What a huge difference the controller makes. In this case, the "faster" (and newer) controller is not better. Another minor complaint, a slight jerky-ness while watching DVDs, has also all but disappeared.