is this two profiles or two accounts in a single profile (I have no idea why anyone would create a new profile for this an I certainly hope you have not.)

When I changed web hosts, I was told that the only way I could access my IMAP emails from my original host via Thunderbird was to create a second profile in my account and then migrate the messages. What wasn't clear was that I had to do this in "Local Folders", not in my name@domain inbox, so I didn't know why I kept getting those error messages. Once I figured out to import via the Local Folders section, I got my messages so my old ones are there, and I can get new ones. Once everything is moved and functioning properly, I can delete the old default profile.

The issue is that IMAP folder are dynamically synchronized to the host. They must be moved at some point to local folders to prevent the host from deleting them, and to make them remain visible when you delete the IMAP account (the associated folders go with it.)

The usual approach is to simply add a new account (file menu [alt+F] > new > existing mail account) and have both imap accounts visible at the same time.

You can then drag mails from account to account directly to achieve the transfer without the use of the import export tools, or any major difficulties.

Personally I would go back to your original profile, add the new IMAP account and abandon the transfer attempt.

Thanks -- a little late, since the other advice I got was the opposite, saying to add another profile. And once I got everything in, it worked OK. It was the 'local folders' bit that wasn't mentioned clearly enough (for me, an obvious non-techie) that created the problem, and once I used that, the import worked fine.