I just got done listening to the latest episode of the Order 66 Podcast - Social Engineering. Jay Little was the guest speaker (I believe he's lead designer on Edge of the Empire) so you know you're getting good info. Four main points were hit upon that I think bears repeating.
The first has to do with how social skills in Adversary stat blocks are handled. A lot of them have ranks in the "influence skill group" (Charm, Coerce, Deceit, Leadership, and Negotiate), but generally speaking most players don't take too kindly to having NPCs roll checks like that since they influence the PC's response to the situation. The solution is so obvious that I can't believe I didn't think of it before (especially since I'd considered Discipline and Cool to be kind of underplayed skills before now). Basically, in most situations if the NPC is trying to Coerce, Deceive, or appeal to authority (Leadership) the GM should call upon the player to make a Discipline check (with difficulty equal to the NPCs ranks in the relevant skill). Likewise the player would roll Cool if an NPC tries to Charm them or Negotiate with them. This way the player is the one rolling the dice (actively participating), so they feel as though they're the one in control of the situation. In other words, it puts the narrative spotlight on the heroes, which is perfect.
Second is something that I had thought of doing anyways, but it was nice to hear Jay Little himself suggest it. That is to say, skill/ability pairings, as well as which skills oppose each other, are more suggestions than hard and fast rules. If the Wookie wants to get in your face and flex those giant hairy arms he's free to make a Coerce check using Brawn instead of Willpower as the associated attribute. Likewise sometimes it might make more sense for Negotiate to be opposed by the opponent's Negotiate instead of Cool.
Third, skill checks in Edge of the Empire generate a different narrative pace than binary skill checks in other systems. That is to say, the scene is set up and actions are described in a D20 system (for example), and then the skill check comes in at the end to resolve how everything played out. In Edge of the Empire, the skill check occupies the middle of a "scene." There's a set-up with actions described, but after the dice are rolled there's more story. What's more, those story elements are dependent not only on the die roll, but the approach taken (what skill is used). Adjudication of success, failure, advantage, threat, triumph, and despair will potentially be very different depending on whether you used Coerce vs Charm, for example. What skill you decide to use has more chances to affect the story going forward, often in multiple ways.
Finally, the most mind-blowing concept was the idea of social combat that works exactly the same as physical combat. Because combat checks work exactly the same way as any other skill checks (unlike D20 systems where attacks, defenses, and skills all scale differently) this is absolutely possible. You'd roll initiative as normal, but instead of working with Ranged Light, Ranged Heavy, Brawl, Melee, and Gunnery you'd use the influence skill group (Charm, Coerce, Deceit, Leadership, and Negotiate), and potentially other relevant skills based on the situation as "weapons." Instead of inflicting wounds, successes (and potentially advantage) would deal strain. The losers would be unlikely to pass out when exceeding their strain threshold, but it would represent the fact that they're pretty much spent. If you want to get really creative you could even use your Willpower (as opposed to Brawn) as a "social Soak value," but without the equivalent of a base weapon damage this could potentially lead to really long, drawn out combats unless you come up with a system for assigning a base strain damage to your skill checks. Personally while I think the Willpower = social Soak is a really cool concept, the added layer of complexity is probably not worth it.