Thank you Walt and Charles for your efforts. Of all the weird problems to have... But then, I do tend to get the odd ones.
I did as suggested and reinstalled the reader apps (FBReader & Aldiko) and checked the defaults - none were set. I then cleared data on everything involved (including CC), still no luck. I still got the "no app answering the call" dialog on epubs. Interestingly, I do now get options for mobi (including Moon+), which was not the case yesterday. So now we're down to just epubs being an issue.
In the file browser, selecting an epub now presents all expected options - FBreader, Moon+, and Aldiko. Just for kicks, I selected to use Moon+ as the default. Went back to CC, cleared data, rescanned, and still "no answer".
Since I was looking for an excuse to tinker anyway, maybe today is a good day to install a custom ROM. I've been unlocked and rooted since day two of having the tablet, so all I needed was a reason. I'm gonna go make a nandroid and get started.