In my case, FWIW, I used an IMAP-compatible mail client (Outlook), and dragged my crud from one mailbox to the other. I did have some issues where mail conversations where different messages were under different labels ended up in not copying fully over, but that's partly because I migrated section by section.

Also, of course, note that if you have a mail message under two Gmail labels, and use IMAP to copy your folders, you'll probably end up with two copies of that message.

Migrating out of Gmail, FWIW, is still a pain because they are so nonstandard now.

But I never had an issue with the dates on the emails.