There are many ways of doing it, yours is just as good.
There are 2 ways to extract from Nandub/VirtualDUB. One is an actual WAV converted from the audio track and the other is to just demux it out. Setting Audio to Full Processing Mode actaully converts the audio to a WAV file. (Remember VirtualDUB cant handle AC3 or VBR MP3's, Nandub & VirtualDubMod can)
But the best is to demux the audio out by leaving Audio set to Direct Stream Copy and hit Save WAV. The file is NOT a wav file but whatever it is in the avi. GSPOT will tell you exactly what the audio is in the avi. So save as *.MP3 or *.AC3 or whatever, then convert with BeSweet.
The main thing is to extract it out fully, then convert it.
You can also just load the AVI into an audio editor like GoldenWave or CoolEdit and save out the audio as a WAV file.
Out of the last 20-30 avi's that I've converted, I can remember 1 that I had to extract the audio manually via Nandub. All the rest have converted flawlessly. If you have 9 out of 10 with problems then I suggest you look at your download manager, etc. Have you tried running them through DixFix or DivXRepair?