I'm having the exact same issue. The Krynn are attacking with two transports in two separate fleets. It cycled through both pre-invasion screens (where I just select START) and then the same screen flashes but with "waiting for other player" instead of START at the bottom. Nothing occurs afterwards.
The game doesn't appear to be frozen. Game animations are still running. If I hover over the attacker's tactics, it pulls up the tactic's description. Task manager shows the game running. Just to be sure, I restarted the game several times but it is doing this every time.
I'm running the v1.0 of the game.
Other than this issue, great game so far.
