It could be how compressed audio is being encoded carrying something over from the source.
1. Is the DVD you author in DVDA using PCM or AC-3?

I use the WinFast TV2000XP with an AVI selected codec pair (MJPEG PICvideo and uncompressed PCM 48kHz) in a 3rd party TiVO-like app called Showshifter (here). This locks the audio very nicely into the AVI, and I've done this with both Hauppauge and WinFast cards and various combinations of audio hardware (onboard and PCI audio). Gone are the days where you should suffer sync problems, when the software is written correctly.

I've actually been happy with my file dabblings using the LeadTek PVR software. However I wanted an editable format and had already followed the lifecycle of Showshifter and didn't want to invest my mental processes on something else. I believe the LeadTek software uses the Ligos encoder, possibly using MPEG-1-layer2 for the audio. I'm not near my edit PC to check.

2. If you play the disc without skipping chapters, it plays back fine?
Incidentally, if it does then the timing can't really be solely based on the Vegas/DVD timeline and must have some impact from its source format.

I'd not pay too much attention to the DVDA preview window for judging what has gone faulty with audio sync. It is quite common for good media and targets to actually not quite be in perfect sync in DVDA.

Nero DVD-Video profile will currently alert you that reallocation has failed. Funny that this is pretty well only with DVD-A files. My neodvdplus processed authoring seems to be OK. I think Sony say it is a Nero thing. Perhaps it is, but it worries me on the compatibility front. Just not enough to stop using DVD-A. I'm fairly confident that although the warning might be with regard to the timing, the good discs also warn this all the time, so ....?

The WinFast capture is capable of 720x480 NTSC 4:2:2 YUY2 and your audio card is probably OK capturing 48kHz 16bit stereo from at least it's line level inputs. I'd personally buy ShowShifter and use either the built-in PICvideo codec for AVI and PCM audio. It'll reduce your artifacting, as I assume you are not doing straight cuts before you go into any of these Sony products. It might also clear up the audio sync problem which sounds like an interop problem between the Ligos encoder and Sony's MainConcept-SDK+ directshow audio engine.

There are other capture apps that support D1 on Bt878/Cx-Fusion chipsets. Just that I can almost promise you that you'll get sprocketed video+audio with Showshifter in its AVI mode (PICvideo MJPEG Q=17 (almost DV quality - subjectively)for PII 400 through Q=19 (DV) for PIII 900, and Q20 PIV 1.6GHz (almost DVCPro50) ). Ensure that you have quality cables (ideally triple shielded) and short runs.