William,
Have you set up any Smart Mailboxes? If so, where?
What you have reported about the contents of the INBOX.mbox for your account with prior ISP, is consistent with what I was saying about leftover files. See:
http://docs.info.apple.com/article.html?artnum=301315
All xxxx.mbox folders should be cleaned up have ONLY a file named Info.plist, and a folder named Messages -- the latter contains the actual message content, and has a file for each message. All the others should have last date modified info consistent with when you upgraded.
However, I have not seen the leftover files cause the specific situation you have with Mail being sent, repeatedly, upon startup.
Let me know when you have completed the cleanup of all your xxxx.mbox folders, and also about whether you have used Smart Mailboxes anywhere.
Ernie