Feds are stuck to random drops ><. Not craftable, no mission repeat award.
Best option is running a KDF through that mission and mailing over. The mission that KDF has that gives a core for repeat isn't even a NEW mission but an old one with a new reward list. WHY didn't Fed's get that treatment?
There is no replayable mission rewarding a Warp Core. I looked trough all episodes, and there is no mission thats rewarding a Warp Core now. But there are, thats really interesting, many missions rewarding a Pollyalloy Armor with extended Plasma Resistance. And there are also many awesome ship- and even some awesome grounditems, but there is, still, no Warp Core. Your only choise is playing missions and hoping to get a good one, or to buy a more or less good one for EC or a better one for Dilithium, or a really awesome one for a bunch of EC using the Exchange,
I find buying a blue Mk X core with some helpful stats, like [eff] or [X->Y] is a good place to start out, then when you can afford it go up to XI/XII and very rare, if you can. You can easily spend more EC on a mk XII very rare core than a whole lockbox ship.