I should clarify above. When I say "between servers" I actually mean between TB on my local PC and the google server since I'm using POP with local messages.

The Gmail setting should be OAUTH2, not normal password. First thing to do is update the gmail account properly. The transfer is encrypted when set up properly. You mentioned the testing went ok. Was that a handful of messages or hundreds or thousands? If doing a lot, I suggest doing in small groups, or create a manual filter to administer the update. And spot check afterwards that complete messages are uploaded.

Only a few dozen messages.

OAUTH2 wasn't an available selection during setup process, which was strange. I've selected it now and logged into Google.

I was using the Google app password feature prior to. 

Does the lack of OAUTH2 setup make the transfer process somehow lose its encrypted connection despite SSL/TLS being set? Or is it more of a general security best practice to avoid a locally stored password on TB that could be compromised?

I am not technical on the encryption technology; my comment was that accounts without OAUTH2 would soon not be allowed by Google.