The outline in my tutorial has a mistake. Under necessary programs, it lists the MSU Lossless Video Codec. That should be the MSU Screen Capture Lossless Codec.
Also, I fixed the sync problem. Under VirtualDub, go to Video/Frame Rate... and under "Source rate adjustment", click "Change so video and audio durations match". Next, go to Audio and select "Full Processing mode". Click Audio again and select "Compression...". Choose "MPEG Layer-3" and choose "24 kBit/s, 22,050 Hz, Mono".
Not only did this fix the sync problem, the file size went from 16.1MBs to 12.3MBs! I'm just going to replace the file "linked to" in my previous post with this new, smaller file that plays in sync.