Went in early and finally had the flash of insight needed to solve the problem once I realized that I could not ping the mail server from my own computer. Took a look in the server's control panel, and sure enough, Microsoft, in it's infinite patronizing wisdom turned Windows Firewall back on at some point while I was doing all the updates to XP, thus protecting the server from detection by nasty malware infested computers, not to mention every other frelling computer on the network. It's XP Professional, people! It's designed to be used by folks who already have a firewall on their network.
Once that was out of the way, the only other hurdle was that the new server software requires SMTP authentication, which the old one didn't, so I had to run around checking off the little box in everyone's Outlook settings to do just that, and then figuring out how to do the same with our fax machines and other odd SMTP sources.
Still seeing some odd behaviors here and there (the fabled "No transport provider" error has been popping up a lot), but other than that things seem to be working.