Thanks guys...
Nope, no background tasks to speak of; no changes in DNS, lighttpd, or Moodle configs. The servers do also handle our website, but the website is cached up the wazoo and places practically no load on the app or data servers.
DB engine switch was done through our server db console, not Moodle; but we switched back to MyISAM again after a few days. And yeah, we're still running 2.0, haven't upgraded. Moodle is not a big project for us, and its few users are reluctant to change, so we tend to leave Moodle alone as much as possible. A "few months" is no time at all for us, because we just don't touch it.
Yeah, none of the obvious explanations for a speed-up seem to apply. I told you it was "mysterious". Since I can't rely on these speed increases, we will go ahead with our switch to Postgres. We are looking at 2.2 as well.
Thanks again!