First of all, thank you to everyone for taking the time to read and respond -- it is appreciated.
I did run Stinger and Symantec's W32 Sober Removal tool after it became clear that the machine was still compromised. I also ran Trend Micro's online Housecall. Stinger did find infections in the System Restore points, but otherwise nothing new.
I'm starting to agree with DavidR that this may be a non viral attack. The system does have updated versions of Ad-Aware, Spybot Search & Destroy, and Spyware Blaster installed and active. Ad-Aware and Spybot found nothing. I'm not familiar with Ewido Security Suite, but willing to give it a try.
DavidR, the timeout messages don't show the program initiating the emails. I can set the email scanning options in Avast! so that it starts catching them, but at something like 6,000 spams a day the warnings become near constant.
I admit that this machine is proving to be very frustrating, not least because such a gross oversight went on for this long and now is drawing in my time. I'm not far at all from using the "ultimate sanction" on the drive, since at this point a full rebuild would take less time than I've already spent.
Still, would love to figure this out if only for the principle.
Will post any new results once I've installed Ewido Security Suite.
Thanks again!
Jacob