So being a relatively new fan to PWG here's what I see happening. First we have 6 of the eventual ten members involved in this.
From my take, guys like Chris Hero, The Dynasty, Strong and Davey Richards are all strong solo characters. None really need a group other than Machine Gun and Lost. Scott Lost is getting pushed towards an eventual PWG Title Shot, so teaming with Omega wouldn't work, and I feel like the original 3 will be the most important 3, as in Kendrick is higher on the food chain than Lost. Lost has already been held down by Joey Ryan, so it wouldn't make much sense for him to join another faction. Machine gun I haven't seen enough of, but I'm assuming he's not the type of guy qualified for the storyline of the year in PWG.
Seeing as the factions include all the champions, I think it's important the face team has a tag team on it. The simplest and most qualified to challenge the Young Bucks is 2 Skinny Black Guys. Tornado seems like a must on Team Omega. I'd like to experience heel Tornado at his finest, but I think he hasn't been face too long, and is needed much more on the face side.
I really like the idea of Chuck Taylor on the heel team. Not sure he is strong enough to be on his own at this point, and everything you guys described made him perfect for Team Bucks/Kendrick.
Assuming this feud last awhile and assuming Kendrick and Omega is the eventual ending of the feud, I think it's important to have a guy the fans will want to see against the captain other than the opposing leader. Omega already has former teammate Chuck Taylor. That's why the fifth spot on Team Omega should go to Paul London. London vs Kendrick may be more money than Omega vs Kendrick, so this seems like a no brainer to me.
If the eventual leadup ends up Kendrick/London, The heels need a big time player for their fifth member. In this scenario Scott Lost would work out perfectly, but not sure how team would be built, as it seems odd to appoint Lost the leader right off the bat. I think Necro Butcher would be a very intriguing matchup for Omega, and he would fit the mold of guy that takes a back seat, but ends up leading perfectly (At least for me). The perfect solution here would be Super Dragon. He would join up to make his return in a big fashion. Him and Omega would also be a huge draw I think. The only problem with this is, I don't know when/if he is ever coming back. He is still listed on the roster, and his Wikipedia page didn't seem to list his injury as anything career ending, but I really have no clue what happened. Another guy that intrigues me is PAC. I like what I've seen of him, but I'm not sure how free he is, seeing as he appears fairly frequently in Dragon Gate.
I think Omega's team for the most part is a sure thing (at least logically to me) where the Heel team seems to really only have 4 that make sense (again to me)
Scott Lost/Necro/Super Dragon/PAC