After waiting several more days for CSoft to respond - through which time my site remained down - I lost patience and decided to change hosts.
So I went with them. Set up the account on Friday. All that fun stuff all over again, switching DNS, learning a new panel (this time, it's ensim pro), setting up the database and uploading the data (which, uncompressed, is 272 megabytes (but an impressive 42 megabytes compressed)).
Stuff began coming back online today. All data requests (for pages, posts, etc - anything from page.cgi) are responding, albeit without pretty CSS formatting. All redirects (edurss02.cgi) are functioning again. All archive pages (that's about 8,000 pages, mostly OLDaily and Edu_RSS archives).
Oh, and hey - the server isn't crashing. There are no runaway perl scripts, even though I'm using exactly the same code. The site is responding nicely, so far (knock on wood, etc) despite being hit pretty hard by the search engines (I found that Yahoo has a nice robots.txt command to slow down its slurping; nothing from Google though).
What's next? I need to get the contents of the /files directory uploaded - that's my biggest gap at the moment. Some of the smaller directories as well. I won't be replacing the massive /photos directory, but I will write some redirects to Flickr (I get about three hits a month on those, so I'm not worried). Then I need to get the newsletters back up and running.
It just goes to show - sometimes you can plan something for a month, have it crash and burn, and start over from scratch working on the fly and do the same thing in three days. That's life on the internet.
The people at ev1servers.net have been, I might add, very responsive and helpful.