Hahahah , ... been there done that as the saying goes.
My old Logitech is stuck on the back of a black plastic film can. It did work surprisingly well. The Logitech software gave decent enough control over the exposure levels and I think I was using Amcap to record the avi files but any capture software should work.
Biggest problem may be to get reasonable tracking during the recording period so the moon does not drift too far within the frame because the stacking software will have difficulties aligning them. I was lucky with an old EQ2 mount I modded with a drive motor and set up outside on a marked baseline. I also used a heavy weight slung under the tripod to keep it all stable and still.
IMHO it's a good cheap way to whet your appetite with astrophotography and great for the DIY spirit of it all. But be careful, it is addictive and gets expensive real fast cos you will want to do better as I have found out.
Go for it, good luck and show us the results please.
P.S. I may end up using my old Logitech in a guide cam setup btw, still experimenting.
P.P.S. You may want to blacken the inside of the of the old barlow to kill any light reflections. My old black plastic film can was matt inside, no problem but you will have the gain of the camera well turned up so anything with a photon attached may get captured.