Thanks so much for the advice, Kerry56. In case anyone else has the same issue, this is how things went:
I decided to start by making an NTSC so testing would be easier.
1) Tried DVD Flick. This looked good, but the audio was partially missing.
2) Tried AVStoDVD. DVD looked good again. Audio was there throughout this time, but out of sync by about half a second.
3) Tried FAVC. Used there default optimization setting for quality. Took a really long time, but the result was wonderful. Made a PAL version which worked in VLC and sent it to a friend in Europe for validation.