Thanks, as always, M for the reply. After posting I realized that there would probably be some sort of Azalea society that would be able to offer some very specialized help. Indeed there is such a society [azaleas.org] who even had an email address that went out to all of their list-serve subscribers. So I described my problem and sent the picture and was told that it is a combination of overwatering and lace bugs! Here is specifically what they said about the latter:
If you examine the reverse side of the leaves, you should see lace bugs (only 2-3 mm in size) and lots of small dark fecal spots.
Although I saw no bugs, there were a lot of brown spots. Their suggested remedy is soapy water on the underside of the leaves, so I’m going to give that a whirl this weekend. Hopefully it’s not too late.