let me solve your quandry. Trigger pull makes no difference in anything but accuracy for a competent officer.
i carry a 1911 with maybe all of a 3-3.5 pound trigger with zero take-up, almost no travel, and zero over travel. I have never accidentally shot any unsuspecting people with it because i have never EVER had my safety off on duty. Safety comes off and finger goes on the trigger a 10th of a second before i dead somebody.
Never had to dead somebody so trigger pull is completely inconsequential.
My glock 21 has a 3.5 trigger too. Never shot a hole in my leg with that one either.
Your gun could have one of those electronic paintball electronic triggers and it wouldnt matter if you trained with it and used it properly.
I do however get a big kick out of going to the range with other cops and letting them shoot my gun. Usually they're like "holy shit, i hit something i was aiming at with proper stance, breathing, sight picture and trigger control ! and your trigger is freaking dangerous!" and then i let them go back to missing with NY1 triggers.