I agree with continuing with the Padme team, especially since you have unlocked GK. Putting gear into JKA and Ahsoka will help with fleets once you can unlock Kenobi's capital ship. If you get both his and GG's, then you have the top two capital ships. Just need the two droid ships to go with GG's capital.
Going for GAS is also a good idea over switching to JKR. For a CLS team, you really need both Chewie's and C-3PO, which aren't the easiest to get when you are farming other stuff. CLS, Han, Chewie's and C-3PO are a good counter to a Padme team.
Since you are on a newer shard, you will probably find the first one to a GL will rule for a while. You can research counters. I would bet people would go with SLKR first, but that is probably a ways off unless you have some big spenders.