The thing about Poe that I think many are missing, and specificly about the Poe vs Poe match-up, is that your Poe actually gets worse the more of your teammembers that move on turn 7.
The reason we include Poe is for the turnmeter reduction and how that lets us attack before the enemy. So we already have the 50/50 that our Poe will act after the enemy Poe. Then if we run a team of 4 turn 7 damagedealers, we also have the chance that our Poe actually goes after all or most of our dps and then he is just a taunt. And while others might like to include someone that is great in less than half the matches, I don't like the RNG of such a character.
Also I think that any teamcomposition that wants to get a good match-up against the Poe teams will have to adjust for the times when their Poe acts early and you have to start 5v3. The only way you have a good chance of getting out of that one is if you can give turnmeter to your damagedealers so while the enemy gets the first volley, you get the second and third.
Therefor I'm considering a team that might look like:
Dooku (good against Qui-Gon Jin that I expect a lot of)
Rey (one-shot potential before Poe)
Geonosian Soldier (one-shot potential before Poe)
Qui-Gon Jin (Can really bolster your second volley if he lives)
Stormtrooper Han (Has a chance of messing up turnorder if enemy uses aoe or is targeted, can stage the comeback with turnmeter to the team)