Maybe they were like the Flying Tigers somewhat?
That would have been terrific. Volunteers to take on the First Order to give the Republic non attribution.
I would have even liked for to be maybe the military arm of the Rebellion is so loyal to General Leia that they were "rebelling" against the Republic who didn't really consider the First Order a threat. That threat becomes very real and Leia is vindicated once Starkiller Base is operational.
Make the crazy Han/Finn monster chase scene 60 seconds shorter and add one minute of dialogue with Leia and some other folks and they could have raised the stakes and painted a more complete picture easily.
Stonesean's post sums up why I don't get the love for FA. It was ok, maybe 6/10 but I seem to be in the minority.
The problems with the story were mitigated by what AH mentioned.
The prequels seemed like Lucas was TRYING to make a "Star Wars" movie and not entirely succeeding. There are many sequences in the prequels that are terrific, but dispersed among many bad sequences as well. Also: "Duel of The Fates" from Phantom Menace might be my favorite piece of John Williams music. Period.
Force Awakens was not an attempt at a Star Wars movie, it WAS a Star Wars movie. The "magic" that was lacking in the prequels for me was there in FA. Plus, (insert member berries voice here) Chewie was always my favorite and he had a prominent role. I'd probably give it a 7.9-8/10. I liked it better than AH.
That "magic" was also there in Rogue One. And I totally LOVED the "Dirty Dozen" vibe I got from the last 1/3rd of the movie. A suicide mission that was actually a suicide mission.