In case anyone else is running into this issue. I spent an hour on chat with Apple yesterday and another hour today with no luck. I felt like if there was a way to wipe the activity app and then put it back and start over, it might work, but they weren't into that option. Maybe it just isn't possible.
Last night, I erased the iPhone and restored to a backup from 2 weeks ago (the only time I've thought my iPhone's failure to regularly back up on the automated schedule was a plus). After a brisk walk today, I got the first achievement badge. So, the problem seems to be fixed. Now I just have to resync all my media to the phone.