Okay, assuming that I have the power in game to control the actions of the Northern Alliance this is what I'd do under your given restrictions.
1. Don't attack Coria, and let Coria's agreement with Eston force the war to be a standoff at Cantril.
2. Negotiate peace with CE on neutral terms. (I believe that this would have been possible since it was just a standoff for real life months.)
3. Bide your time, and watch the diplomacy of the south. Nudge diplomacy into a war between Suville, Strombran, Caergoth, and Carelia. (with possible participation from CE and/or Tara)
4. The above conflict would have placed Tara and CE on opposing sides. Use that to drive a wedge in the CE, Tara alliance.
5. Ally the north with Coria (which was very possible under former conditions, a lot more difficult now)
6. Along with Coria attack south with the unified north while CE and Tara are split. However, don't attack both of them. Focus on war, and make it clear your intentions in the war. Not just "reduce the power of CE, or destroy CE". Attack either CE or Tara, while all of their allies are distracted. Tara would be easier, but CE would be just as susceptible.
7. Try and break the federation permanently by offering the other side an alliance in return for very favorable terms in whatever area of the map that they want.
That is how you beat CE. However, it all falls apart because I made the simple assumption I could unify the north's opinion. But if the north wanted to win, that's what they do. You don't just attack "CE's powerbase" with nameless intentions because that will provoke a huge backlash.
Perhaps just claim a single duchy (and state that at the beginning of the war), or something. That way they know what happens if they surrender. You can only afford to not make terms if you're like CE and can enforce whatever you want.
Cogent and well reasoned. It's a good plan, though it could fall apart in any number of places even if you did manage to achieve unity in the north.
Unfortunately, the necessary political preconditions for this plan were not all in place at the time I made my decision. It's hard for me to remember exactly what was going on down south at the time, but Carelia was still alive and kicking (albeit definitely losing), Strombran had not yet been founded, and Caergoth was still in one piece if I recall correctly. Even if you advance the timeline in the south somewhat, I'm certain that most of the pieces you're playing with were not available.
Basically, it's easy to see all the parts necessary to your plan now. Back then, they mostly didn't exist. By the time they emerged from the fog of war, the die was already cast.
