I contacted my host, and it turns out the problem was caused by a runaway spam filtering process that was hogging system resources -- this could have been caused by a spammer attack on the site. It's fixed now, but I'll keep an eye out to make sure it doesn't recur.
The forums are still so young that it may take a while to get a feel for their baseline affect on the server load under various traffic conditions. Another upgrade may or may not be necessary, but let's see how the next week goes.
If anyone does get a "server busy" message, please let me know about it -- you should still be able to access the contact form on the main site under such conditions.
And thanks for the love. It's unfortunate that web servers respond differently to love than people.