OK, it's the usual FAQ-situation, but the questions are different this time

I got this *.avi, codec is DivX (4 i think), when converted to an mpeg stream audio starts OK but drifts and is roughly 21sec behind of the video at the end of the movie (1h 52min)

I read all the relevant posting/howtos here, nothing helped except that I got the warm and cosy feeling of not being alone. So I decided to forget about the 'Why' and simply shorten the audio, using Audacity (under Linux) and its filter "Change Tempo" (or so - I have a german system, maybe in english the menu item is labelled differently; I think it's a SoundTouch tool).

2 Questions:

a) To really help me, the Audacity-tool should change the length of the audio to any given value, say 6689.73 seconds instead of 6888.15. It doesn't. Instead, it computes a new length based on the percentage, which is less accurate. In this example, the percentage is -0,0062%, but it's cut off to 0,0 so that in the end applying the filter results in an audio file as long as the original one.
Is there a way to achieve the desired effect with any other Linux-based tool? Is there any application that will let me change the duration of an audio file to any given value (incl. fractions of seconds) without altering the pitch?

b) To help me understand: How can it be that the audio gets out of sync although the original AVI plays fine? I read a lot of "Playing is different from encoding" and stuff... What I cannot understand, though, is that when avidemux first separates audio from video and saves an MPEG2 video stream and an uncompressed audio, why is it that both files report the same length (1:52:11) and still are out of sync? (Yes, I did do the 'Build VBR time map'-magic; actually, I tried with and without. Same result.) I'd be able to understand if the video was 1:51:50 and the audio 1:52:11, but this isn't so.

I worked 3 days (and my PC 3 additional nights ...) to get the audio as close as I could to the desired length, then I cut black frames out of the video stream every 30mins or so until I thought the result was acceptable. I still believe there has to be another way...
(And, yes, I did try the same with Windows and virtualdub/tmpgenc - same effect, no difference.)