Just to confirm, you're running the latest patch level (Dominions 3.24) with CBM 1.6 enabled (in the mod preferences screen), correct?
One thing you could try: Put up your own 2 player test game on Llamaserver with just you and an AI and see if it works. Try it with this map, and maybe try one with a different map. Or you could try a local game on your machine with this map (I hope it's not the map!).