There are very easy solutions to a fully functioning LAN campaign. Other games of a similar nature have allowed LAN campaigns, such as Battle for Middle Earth 2 - While this was only 2 player it did allow Ai teams to be present. Some ideas:
2 Teams
-A 4 Player game that allows co-operative gameplay. A single faction is controlled by two players and there are two opposing teams. E.g. Britain & Spain. The map is dominated by the Ai factions however battles only occur in real time when the player factions are present (e.g. Britain & Spain). All other battles against Ai are fought in real time scenarios as a priority, however a vote appears which allows the 4 players to vote whether to allow a realtime game. The team not involved will spectate in this case.
Co-op
2-4 players against the Ai. Players can choose to either share control of a faction or choose faction of their own to run which are part of an Allied Factions Group. (e.g. Britain, France, Spain, Italy or India, Pakistan, Asia, Africa). Players cannot fight one another however any Ai battles can be fought with the aid of all 4 players. For instance if Britain encounters a rebel enemy, the other 3 players can assist by controlling assigned squads of units. Or they can spectate or auto-resolve the battle
War
2 players pick a team and play through the campaign, all battles are auto-resolve unless the players vote to real time them. They can form alliances with each other and every other feature that is present in the single campaign.
The trick to this LAN campaign mode is that the assumption is present that players are capable of agreeing with one another regarding how the campaign will play out. 4 friends are likely to play in the same room so they can decide on various settings. Such as...
-Battles: Will battles be Real Time/Auto-Resolve/Spectatable/Co-Op
-Alliances: Will alliances be permanent/breakable
I think it could work and it is a lot better than delivering the same thing we've always had