Finally some good news from Segpub regarding the timeouts and slow response times (3 minutes, 38 seconds for a plain HTML file?!) that have been sporadically plaguing my poor sites for months. From a mailing list email addressed to folks on my server:

The issues with [your server] unfortunately are related to search bots and a mix of other nasty traffic. We’re working really hard to get ontop [sic] of these and are pretty close to having everything resolved and back to normal.

Nasty traffic? That's not a nice thing to call my Nonsense section! ;).

The problem is, because my sites slowed down to a crawl but still eventually loaded, they don't count these problems as downtime which means they won't be providing me any free months as stipulated in their uptime guarantee. Sneaky.