Seacost — thanks for the tip. I tried to hold off on that for a while, because I had already reuploaded a new wordpress install and reinstalled all plugins once. The fact that the problem had disappeared then relapsed made us suspicious of something on our shared host.
Long story short, a friend found a similar problem with someone else who used our host (Surpass, for what it’s worth.) There was an issue with “modsecurity” on their end….we submitted a ticket and asked them if any changes to configuration had been made and described our problem. Within a day or so, they sent us a notice that there was an issue that they fixed. Not any helpful detail, but it was fixed.
I hope this helps somewhat!