Further correspondence with the system administrators at TextDrive reveals that slow queries were not the problem, but rather sheer volume of queries. Basically, the system adminstrator looked at the CPU utilization on the machine, then disabled my site and continued to watch it and the utilization went down. As he points out in his email message, I only have about 7000 entries and only a few hundred comments, so the size of the database isn’t a problem.
Jay Allen responded to my previous post on this topic saying that I shouldn’t be seeing these problems with a site my size, even if everything is published dynamically. (Most things are, but the home page, which gets the most traffic, is not.) As far as plugins go, there’s not much going on. The only plugin I installed myself is Markdown, and the others that are installed are Nofollow, SpamLookup, and Template Backup and Refresh.
In any case, the limits imposed on the account are lifted for now, pending further problems. I am curious to know why this problem is happening in the first place, so hopefully the answer will reveal itself.
Update: In order to be a team player, I’ve enabled page level caching in Movable Type for the site. Hopefully that will improve things from TextDrive’s perspective and make the site zippier for users as well.