The LF-D311 does not support DVD-RW. It supports DVD-RAM and DVD-R, the latter of which can be used to back up DVD games. However, I thought you needed a hacked PS2, no? Why bother though? Do you have a 3 year old brother slobbering on your discs or something?
I can confirm that DVD-R movies do play back fine in the PS2. I made some home videos that work on the PS2. It's a bit more picky with media though. Cheap media doesn't work well with the PS2.