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A workaround is to set up a desktop email client - allow it to fully sync, then use the desktop email client to export your email and import to another account.

Google rate limiting and restricting access to your own data is pretty awful. They are similarly terrible about OAuth permissions for 3rd parties - some companies are allowed to export data on behalf of customers while others are not.

Doing this via an email client is going to be really slow. Use something like fetchmail.

Fire up gyb [0] now, and by the time this (or whatever solution you want) is ready for an import, you'll be done.

0. https://github.com/jay0lee/got-your-back

Why this and not takeout?

If it's a one-time thing, then even it taking weeks is quite acceptable.

Would Google Takeout not suffice in this, maybe after some post-processing?