I would assume you are covered if you have the NM tag and it is tagged 100% legal in NM, however I say better safe than sorry, call the CO game and fish to confirm. Personally I’d base it on the state I’m hunting in for the proof of sex, but you have to be careful cause transporting a full skull...
That sounds like an exciting tactic! What do you do if the herd bull clams up, or starts moving his herd away? I assume chase, but do you continue with the same tactic of the shooter cow calling while chasing?