I think some of the problems in understanding some things here, is some people seem to have varying forms of tunnel vision and are fixated on certain ideas and/or scenarios, and arent seeing the big picture.
How many who insist on only worrying about the 3/3/3 thing, actually realistically practice just for that, shooting up close from a holster or however they carry their guns, while moving and shooting rapidly and repeatedly, without sights? It doesn't matter what sights are on the gun when you're shooting without using them, but you do have to practice shooting that way if you want to be the least bit competent and proficient at it. You also have to be able to do it without thinking about doing it.
And what do you do when you get something beyond contact distances and you "have" to respond?
The whole point here is being prepared, for whatever you "might" get. Not just what you're constantly told you "will" get. It shouldn't matter what gun you have, or what the sights are, "you" should be able to shoot however necessary and called on to do so in the moment, in a real world environment, whether or not you think its fair or what you're ready, or not, for. That requires a lot of actual, constant hard work from you, and that's just trying to keep up. Its not the Matrix and you cant absorb the skills necessary from reading and talking about it on the web.
Reasonable and realistic self-defense type distances are ANY that you might get and have to respond to. Self defense is self defense.
And contrary to what a lot seem to want to tell you, this isn't likely going to be "your" choice, and you "just might" actually have to deal with things beyond what you've been constantly told you'll get, let alone trained for, like it or not. The real question is, are you competent and prepared enough to deal with things across the board and beyond the 3 feet you're constantly told is all you will get, should you need to?
Big picture.
The first gun I put a red dot on was a SIG P320 and soon after that, a Glock 47 and 19. I pick up the dot with all of them the same, and the grip angle isn't an issue. Its just a matter of presenting the gun up in a manner that your eye picks up the dot while you're focused on the target. Focus is on the target and dot, not the gun or the dot.
Initially for me, forgetting about the front sight and presenting the gun as I would when I point shoot over top of the gun, made things a lot easier for me. The sight/dot is basically in the same plane as my line of sight shooting that way. If you do the same with iron sights, and roll your head down slightly after the gun is presented, the irons are usually lined up pretty good and right on there.
Personally, I think if the grip angle thing is all in your head and you just haven't shot the different guns enough to have the index buried in your brain. I regularly shoot a number of different guns, with differing grip angles, and the difference in impact between the first round or two hits when switching between them and shooting reactively on target is usually minimal and wouldn't make a difference. If you track the front sight or target/dot as you present the gun, you don't see a difference at all. And any rounds after the first, your brain is already on it and its taken care of things.