Planescape Board Game?

Planescape Monopoly!!

Factols as playing pieces, Getting Mazed takes the place of Go To Jail, and the Chance Cards and Community Chest are replaced by Wheels of Mechanus/ Whims of Limbo.

OK, that was pretty lame... sorry

Make it focused on the Kriegstanz and base it in Sigil. Each player chooses a faction to play and they each take turns either gathering up more followers/believers, making plays for city locations and doing what they can to disrupt the other factions. The winner is the person who manages to either capture all of the city locations for their faction, or have enough believers in the city to overwhelm the other factions.

You could also have a counter that represents how fed up the LoP is with the Kriegstanz. When it reaches a certain point, all the factions are expelled from the city and the game is over, making it a lose condition for everybody. Cooperation between factions could bring the counter down at the cost of sacrificing any gains a given faction may have made.

For the Kriegstanz-styled game, you could take a cue from the Illuminati card/board game and give each faction its own particular win conditions and different abilities for achieving those ends.

I'd be wary about trying to incorporate too many aspects of the setting into one game. I'd suggest picking a single aspect to focus on and expand it.

For instance, you could make an interesting game based around the Great Modron March. Sixteen different planes to pass through, and for each one there would be a conflict that the players would have to successfully navigate. The early planes would be easy to get through and the difficulty would ramp up as they progressed. Success for the game would be getting to back to Mechanus with a certain number of Modron left in the march (or maybe even just one).

Another, more obvious game, would be to base it on the Blood War. But, if you're wanting something different than that, you could base a game on the different elemental factions on the Inner Planes. Or maybe make it Efreet vs. Djinn vs. Dao vs. Marid.

Or, rather than a game based on head-to-head conflict between the players, you could make it a cooperative game. Save Curst from sliding to Carceri! The players have to move about the board and perform different actions to ensure the city doesn't slip across the planar boundary.

Just tossing ideas out right now. Hopefully something will catch your eye.