You are correct about InCD only working with re-writable media. However, everything I have been able to find out indicates that Direct CD only works with CD-Rs/RWs. It does not work with DVD discs at all. So you might as well uninstall it.
XP's built in burning function also only works with CDs, not DVDs so that is of no use to you either.
I am not sure if there is any product out there that lets you drag and drop to DVD+R/-R discs. I am not really sure of the benefit of doing that, since it is essentially the same thing as burning using multi-sessions.
In your position, I would get hold of DVD-RAM discs (which your drive supports) and which were specifically designed for drag and drop type use. I'd use it till the disc is full and then just use Nero to copy the whole disc over to a DVD+R or DVD-R disc.