Switch out Ki for General Skywalker, and Rex for Dash. Ferus should be replaced by Lobot. Skybuck has above average odds against the NR.

General Strategy Points.
Use momentum hits to up the damage with Yoda. If an unactivated Mara is near Yoda at the end of a run, leave him there for the next phase. If your opponent uses Ganner/Mara to attack, they aren't going to come close to killing Yoda. Then, swap in Dash afterwards, take the AoO and try to kill Mara. If they don't attack, you swap in a free Rodian Brute and hide for the rest of the round. Repeat a second time, and Yoda has probably done enough to finish the pieces. Generally, you want to use yoda to soften tougher targets, not just kill activations. Make sure you are hitting the Maras and Ganners particularly when you can get away for free (no disruptive). Anakin needs to die early, but just pay attention to his range after you kill a force user and you will be fine.

Specific strategy against Kyle - In and out attacks, take the AoO on Kyle and move out of disruptive, for an immediate swap out in one phase, until Kyle is close to dying. Hit anything not protected by disruptive and force your opponent to move everyone at once in one bubble - that keeps them packed in for easy yoda hits, and makes them predictable. Take out door control first whenever you get the chance to do so easily.

In all matchups, you've got the targets generally backwards. Dodonna and Wedge aren't priority. Their attackers and door control are primary. That's probably your biggest issue. Wasting time trying to track down D and W is simply letting your opponent get Mara/Ganner into position. Mara is not hard to kill with Skybuck. You usually need 1-2 hits with Yoda on her, and Dash can finish her with ease. Anakin is a good finisher as well, but against the NR, Yoda and Dash are used first. Anakin should move up on his own however, as he can often get a backdoor 10 square momentum double off that can finish a key piece, even with disruptive. Against Han GH, this is usually my tactic. Get 20 with yoda on him, finish with Skywalker.

KiBuck works great, it's a matter of positioning for this squad. I ran it yesterday and went 2-1 losing only to David and you can ask anyone I always lose to him anyways. It's about surgical strikes, and I prefer it to Skybuck royally. The key is in how you use the Yobuck on strikes. Avoiding disruptive isn't as hard as it seems. Ki is great for dropping in and doing sweep damage on something I used that tactic 4 or 5 times yesterday killing several of my opponents key pieces. Keep a brute on R2 so that when u swap back you'll still be on him for the next turn. It's harder vs. Evading NR because Rex won't hit as much, but when you see non-evading NR it tends to work better.

Thanks for all the advice - there are two different approaches right? Skybuck is best suited for charging in and destroying things, and Ki-Blast is good if you want a lighter touch?

To clarify, normally I like to try and get tempo control in games - take out some small pieces, and get control. But obviously I need to rethink against New Republic, since it is hard to get to Dodonna (I didn't even try the other night, it's just what I would do if a bad player let me). I do find it hard to want to sacrifice Rex for Mara, if there's a Kol in the squad - I know that it's a good trade otherwise. In one game I took down Anakin and Mara, but I found it very hard to close down Kol with Ki-Adi-Mundi and Ferus - you really need a shooter against him, with his defence of 25, Lightsaber Block, and MOTF2.

I did completely forget about Ki-Adi-Mundi's Lightsaber Sweep too. Thanks for the reminder!