Spoke too soon.
After an hour or so, it read 2.66" in the last hour, and 0.04" in the last 24 hours, and 0 in the week/month.
Total rain read 0.04".
Umm, as far as I can tell, those numbers don't make any sense.
Currently, HWPro is reading 2.59" in the last hour (max of 7.81"), and 0.04" in the last 24 hours, 0 for the week/month, and 0.04" for total.
(Note: It's not raining. The 0.04" is probably from me bumping the unit as I screwed it down to the post again.)
Note that I did do a full factory reset after replacing the batteries.
It seems to me that something is hosed up in the Display unit.