Are you left-handed? The way you describe how you manipulate your weapon sounds like you are a lefty. I don't ever remove my support hand from reloads on my shotgun as I have become proficient with violin loading. I have been able to get my times pretty fast, but when I do it my support hand never leaves the front of the shotgun as I flip it and remove rounds from the shell carrier. What has helped tremendously with that is getting rid of the PG stock on my M4 and putting on a field stock, which I absolutely love. But that is why to me when I have done my drills it feels like I can get a better purchase on a shotgun with say an angled grip, but just because it "feels" like it might be better doesn't mean it is going to. Yet, if it is something that I can work with and train with then fine, if that means my wife and daughters can get a better grip on it and be able to control it better then I am all for it.
We shall see with the shotgun, but I have a foregrip on my rifle and that will never change. I use a c-grip and wrap around three around the front of the rifle and the bottom two fingers use it as leverage, I don't know how else to describe it. I'm not a big fan of the hot buttons. I think the concept is cool, but every time I have run one they always get in the way of having a good grip or I have an accidental light discharge and it drives me crazy, so I pulled them off. Probably could get more comfortable with them if I train more with them, but I honestly feel like it is just another button or contraption to worry about. I know guys that run them amazingly well with no issues after long hours of training, but again each their own. I like my rifle as plain Jane as you can get, not a lot of extra stuff on it.