My site was down and/or unbelievably slow most of the past day or so (in addition to periodically slowing down for no reason for a little while before that). The problem seems to be fixed now. The support folks at my web host suggested turning off the page speed optimization Apache module that I was using because apparently there are some cases where a particular combination of WordPress plugins can cause a conflict, and at least for now the problem seems to have magically vanished once I turned that off.
So (fingers crossed) problems should be fixed and the site should be accessible again!
