I quit hey three years ago for the reason you listed and my hey.com email address forwards to my new address indefinitely. Don’t know if they changed that, but migrating away was pretty easy that way
The real issue for me is moving all the mail over. Since the organization is non standard, imap doesn't map cleanly and it all ends up being a huge mess. I'm not looking forward to getting collections and labels and whatever else untangled.
AFAIK I was able to download the whole archive, but yes, it was a file in my mailbox, syncing it back was too much hassle