What do you mean by a law enforcement background? are you talking about taking a few CJ courses, or actually becoming a police officer first? I think the flight medic would be easier compared to becoming a tactical medic and most places around me the tactical medics are all part time. I've never met one before, but I have read it on one of the departments websites. I have been trying to get into contact with AirCare to do a ride-a-long with them but haven't had much luck with that yet.
I know it's going to be a long road, but I enjoy challenges lol. I tried joining the Army as a medic, but never made it past MEPS.