It is not at all uncommon to just train the actors for real in martial arts as part of the overall filming effort. Similar to making them take guitar lessons if they're playing a lead singer in a band.
I also agree on doing some kind of military drill to make the crew act as if they're a seasoned military unit. Hell, it doesn't even have to be real drill. Make them do Battle Stations drills on the set like it is life and death a few hundred times

You'll start to see some of the teamwork and precision happen.
You can't get somebody to black belt levels quickly, but you can get a lot of the right basic reflexes in pretty quickly. (It's been over 20 years since I did Karate and I never made black belt, but I still drop my center of balance reflexively whenever my footing seems unstable. It helped roller skating/ice skating quite a bit, at least after I realized I had to reverse my reflexes when skating backwards to achieve the same effect)
I wonder if there's a new generation of actresses trained in the Hong Kong style of martial arts...the generation of expats that moved to Vancouver when Hong Kong went back to China in the 90s are both too short and too old for the role, but they certainly had the chops and I'd assume there are younguns wanting the part.
Also seriously. There is a lot of asian talent that would kill to get a starring roll in Hollywood. Asians of all stripes are largely invisible on anything made there, unless it is a vehicle for them (eg a Jet Lee movie). Getting new talent willing to be typecast for low salaries might be easier just to help break that barrier down a bit.