The war of the holy? The heavenly conflict? The celestial rumble?
Yep, you heard right. We want conflict, and lots of it, in the Upper planes.
Let's face it - we use these planes a lot less than the other ones. Even veteran DMs need special effort in order to really involve them. And although we have a lot of brilliant ideas rolling around (we need links to Dave King's material, stat. Also, see pretty much everything in the Portal's section), what we really need is some easily accessible conflict to escalate and play with in order for the novices to become involved with the Upper planes.
The obvious thing is to push the existing cold war into open hostility and even skirmish warfare. This war should not be just an upper planar reflection of the Blood War, which is perfect as it is, but a war of words and behind-the-scenes struggle for the hearts and minds of the good aligned souls of the world. It *is*, in essence, a law/chaos conflict, but there is more to it. Heaven knows (if you pardon the pun) how much conflict we have between people who all consider themselves on the right side in the *real* world. What we need is to bring this sort of drama to the Upper planes.
As mentioned in another thread, it could be mortal-driven. Groups such as the Planes-Militant (perhaps with the more cynical Harmonium behind them), the Guardians (who are great, but we need a new sect for the neutral planes of good), the Verdant guild and the "good" chaotic sects (which are plentiful...Ring-Givers, Sensates, the Fated, to name a few. The last are probably particularly interested in distancing themselves from Sigil politics and showing that they really are good guys). The celestials might find it distasteful to fight each other directly, and in stead use those groups to fight their wars.
On the other hand, isn't it time to let the Eladrin and the Archons have at it a bit? I once wrote about how such a conflict might take place, here: here Discuss.
I'm not sure if I'm just repeating what you said, but I hope there's something original in this:
Physical combat should probably be kept to a minimum, as this would not only be against the concept of good, but also an obvious mirror to the Blood War. Behind-the-scenes sabotage also seems a bit below the celestials. However, overt conversion is not. As you said, if you look at real world religions, mostly all of them consider themselves "good", but they are intent on converting everybody to their form of goodness. So perhaps instead of fighting with swords or words, the celestials fight each other with belief. They try to direct those they save toward law or chaos while releasing them from evil.