I seriously doubt the audio sync problem has anything to do with the burner itself. ConvertXtoDVD is fairly well regarded as a conversion program around here. Do you have the latest version?
If you want to try another conversion program, there are some free ones like FAVC, AVStoDVD and DVDFlick. They aren’t as polished as some of the commercial choices, but work for most people.
Another commercial program to look at would be TMPGenc Authoring Works 4. Not free, but there is a trial for testing.
Are you certain your source files are good? Sometimes corrupt downloads are part of the problem.