The slowness problem should be fixed now (thanks to some help from GoDaddy’s Executive Accounts support staff, but not their normal customer service).
I still do not have the full details, but the root problem was a massive comment/trackback spam attack.
I have initiated two measures to hopefully cut down on comments and trackback spam: I have installed a plugin to close down comments for older posts, and now all comments must first be previewed before they can be posted. Hopefully these measures will help foil bot-driven spam.
If anyone notices any problems, drop me a comment to this post or an e-mail.
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