Exact same thing (I mean, EXACT same, down to the 2 minute timeout, lobby behavior, etc) if my friend hosts.
I've already tried to find someone else to test this with, both on the boards here as well as the GOG boards, to no avail.
I can say that every single other game we play -- without exception -- has worked flawlessly. I'm talking P2P stuff like Warhammer:Gladius, Minecraft (hosted locally), Civ6, AOW:Planetfall, etc. This is the only game that has an issue.
If GalCiv3 needs extra ports opened, or you have some weird hole-punching tech I can bypass by opening up ports explicitly on my router (or his), let me know and I'll give that a try. There's something odd going on in GC3 network code -- again, this worked flawlessly prior to 3.0.
I'll post more if I can think of anything else that might even be remotely helpful.