Here’s what I’ve done in the past:
I’ve used Cinematize to extract the video and audio, then imported it into FCP with no troubles whatsoever. This, of course, doesn’t work with copy-protected DVDs.
Otherwise, I’ve done what you have done, which is to say that I played the DVD through an analog to digital converter, but with one difference from your method: I recorded the DVD on to a DV tape and then used the DV tape my source for digitizing into FCP.
best of luck to you!
Simon