I've never fired out of my weak hand. I'd bet a lot of people contemplating CCW carry haven't fired from their weak hand.
We're not commandos. We are everyday citizens wanting to protect ourselves and our loved ones. Guess we gotta go train now with weak hand now just to make these asshats happy. 
Oh and how the f**k are we supposed to do that? They put all these "standards" we have to meet, yet KHSC's rules and regulations prohibit and bans these types of training.
F**kn A$$h*les.
In the Air Force, back when "small arms for officers" meant "really difficult to grip .38 revolvers" (

), we went through strong & weak side barricade, single and double hand grip, strong & weak handed grip, and standing/prone positions.
There's nothing wrong with adding these variations to your training regimen, because just standing still and repeating the same drill every visit can get old.
In a defensive situation, the only thing you can expect is that nothing will go as expected.
Having said that, if they are testing for proficiency, it should be a straight-forward "normal situation" test. Otherwise, they are just trying to fail people who have little to no experience with firearms other than the basics.