If the Chaos General dies, apply the old Daemon animosity rules, applying them between all differently marked units. Also they could be applied between the different army types, i.e. mortals, beasts and Daemons.
Seeing as its only the General keeping all these mortal enemies together it makes sense that without him they revert to type. Savagely attacking their rivals. Seems pretty full of the Chaos character. This would reward players sticking to one God and army and helping balance the tactical limitations involved.
Placing a downside to taking varied Gods and may help reduce the number of armies taking different God's for tactical reasons rather than for character. Plus its still possible to take all the different Gods and armies in one force just one more reliant on the General.
Any thoughts? Opinions?