I am sure your not making this up so I do take your word. But your tests did show closing the client and restarting it after the main menu loaded worked. So I think it would be a bad idea to add a message in the client showing that.
What baffles me is that the client makes a new connection to the sim every time it asks for information, so when you start the client should not matter. But I will uninstall FSUPIC and see if I can reproduce this.
Edit: I uninstalled FSUIPC, rebooted my machine and did the same procedure and it worked fine. (start client, log into fsa, start fs2020, load flight, push fly in client, worked correctly)