A follow up to my earlier post: I seem to have solved my problem, but as someone else commented, I'm not completely sure how. The big issue was that on the iPad my .mac account thought I was using my ameritech.net (ATT) account as the SMTP "Primary" server and would not allow any changes, including entering a password. So I finally went back to the Mac and changed my .mac server settings there to use only the .mac SMTP server, waited for MobileMe to update the iPad, then was able to change things. (The iPhone4 had not had any of these sending problems.) But I then had to go through each account on both devices and re-enter passwords. Part of this is that Ameritech (ATT) wanted every account "verified". Some would revert to the previous state, but I finally got them all the correct way and things seem to be working.
What I still don't understand is why it went bonkers in the first place. When I got the iPad, everything worked fine, then suddenly, with no software changes, this craziness started!? Oh, well. Have since run the iPad update and things are still working.