Would it hurt my career to go from COCOM to COCOM?

My career was mostly National Guard, but I've had similar experiences, as well as counselling others. Going to another unit almost certainly won't hurt, and can help because of the perception of varied experience. But when you arrive at the new unit, you are an unknown quantity. "If he's any good, why didn't his prior unit find him a promotion opportunity?" You start from zero and have to prove you are better than your peers.

I can't tell you how many young soldiers have asked if they should go to another unit to get a promotion. And unless the promotion is coming requiring a position change (as happened to me, once) my response has always been, "Why would I put you in for a higher slot when I don't know you? You show up at my unit, and tell me you are hot, and I'm supposed to believe it?"

Promotion in the National Guard is the roughest of all services. In order to get a promotion, you have to be fully MOSQ, fully up on PT, marksmanship, etc, fully school qualified (ANCOC in your case), occupying a slot one and ONLY one grade higher than your current grade, and no double slotting permitted. If the guy in the slot you want plans to die in that slot, you are blocked.

Every promotion board I have sat on, multiple MOSs receive significant consideration. If you can get the school for an additional MOS, you have doubled your chances of promotion in whatever unit you are in. Plus it's just about the only way to pass the roadblock I mentioned above. (I retired with MOSs in Infantry, Armor, PSYOP, Intelligence, and Computer Operations, three of which got me a promotion.)

Taking responsibility for your career sets you ahead of the pack already, with so many soldiers willing to let personnel manage their careers. Keep your horizons broad and don't be hesitant about opportunities which cross your path.