Well for starters, you should hold that handgun the same way dry firing at targets, as you would hot shooting. Practice, more practice, muscle memory and grip habit with the same handgun will make you very proficient in drawing, sighing and firing. Both ways of practice, dry or hot, your grip should be the same.
Maybe a grip change is needed or your hand is to small for the grip?
Pictures would help, but IMO I would not get in a habit of using that hand grip, because of the very downsides you mentioned in your original post, and what I have added.