I have read through this entire thread and see posts from people saying Migration Assistant doesn't work. My experience has been positive with Migration Assistant in more than half a dozen migrations, most of them more or less incremental step ups in Mac OS, but also the following ones going from:
10.6.8 to El Capitan 10.11 -- in ONE Migration step, all emails came over including POP and gmail (IMAP)
10.8.5 to Sierra (10.12) -- also no issues in Mail migration
The IT crew in my place of employment, where we have several thousand Macs in use (mostly laptops) standardly uses Migration Assistant to move accounts including email to new Macs when they are replenished, every 2 to 3 years. People here use either Outlook or Apple Mail for their emails. This migration process is successful, people here have many tens of thousands of emails and would never tolerate a partial or incomplete migration.
These piecemeal migrations by hand can be made to work but it sounds problematic and as new OS's come out, likely to not work without more work.
What about this:
(1) Make a clone of the old system (use Super Duper, or CCC, or even Disk Utility)
(2) Boot from and log into the old system clone and basically simplify the user account of interest here so it has NOTHING except email. Remove everything else. Preferences, etc. This is actually not hard to do.
(3) On the new system, use Migration Assistant to migrate ONLY the user from the stripped down clone, all it has is the email left to migrate. If you don't trust Migration Assistant to do other things, uncheck the options to migrate Applications, other Settings, etc. Just that one user and its email.
(4) Then manually add whatever else you want to bring over to the new system after verifying that email still works on the new system and all emails are still there.
I feel like this process might take less time than the tortuous "by hand" email migration efforts described earlier, but I am probably biased because I see Migration Assistant used successfully virtually every day at my workplace.