HA!!! The one thing @KevinM didn’t address was the fact that he is “Goofy Eyed” (left eye dominant and right handed). Please understand that I do not say that in a disparaging way (I am too) but I grew up in the 70’s and 80’s and if your non pushing foot on your skateboard was in the front you were “Goofy Footed”. That said he demonstrates rather nicely the common technique for over coming it, turn your head.
As to range drills “that you can get away with” I have one I will do when tuning up my draw that is more than a little advanced. I will hold the pistol by the barrel in my left hand at “retention position” (roughly 6 - 10 inches in front of my abdomen. I will perform a slow smooth “pretend” draw from the hip and attain a grip in the pistol then transition my left hand to the proper grip.
Here is the advanced part, when my hands hit grip and start to push I fire and continue the straight flat and level push to full extension and fire again, before I hit full extension I close my eyes.
The purpose is not to build speed but to build muscle memory and proprioception (knowing where your body is). The result is two well placed shots that will occur instinctively during a high stress situation and will occur long before getting a sight picture. I highly recommend that you perform several dry fire segments prior to going live so that you have your feet in the correct position to orient yourself to the target. Of course you can also do it with your eyes open.