I certainly did not bother re-verifying files, reinstalling anything, etc. All I did was try connecting to each private server via Direct (input ip address and poirt) or click and connect via server listings. I just tried again on Exiled Lands server and two tries - last time 15+ tries.
As already said, this result implies that some authentication server is working, and that other(s) are not. If all were not then no options would allow access at all.
I have retested connecting to all my private servers and same: try, try, try again and eventually in and without verifying files, replacing mods, reinstalling game, contacting alien overlords, or begging Crom’s indulgences.