After I changed to Blogger-beta, I noticed that I had lost my counter. I went to RightStats to get the code again, and discovered that I had forgotten my login. Rather than play back-and-forth games, I signed up with a new counter on another site - StatCounter. Works fine.
UPDATE: I tried to post the above, and was alerted to a broken tag. The information provided by Blogger-beta was more helpful than Blogger ever was, pinpointing and highlighting the trouble. So, even though I've lost some stuff (my fault), the change appears to have been worthwhile.