FOLLOW-UP: I was able to finally get logged in and transfer my main back to Aether, then log in to Aether on my main and transfer between servers (Cactuar, Adam, etc, not datacenters!) with no issues.

As a test, I ran the following two commands from an elevated command prompt:
--
ipconfig /flushdns
netsh winsock reset
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After a restart, I was able to switch to Dynamis and log into my main account. I logged out so I could transfer the character back to Aether, but got 2002'd when trying to log back into character select. I then ran the commands again and was able to get logged in and back to character select, and transferred main back to Aether. Afterwards, was able to log in on main and I'm stable now. Definitely not going to log out just in case

I understand this may not work for all players, but it's worth a shot. Hopefully this helps SE pinpoint the problem on their end as well