... there is no way I will ever be able to shoot that with iron sights. I can't distinguish the minute differences in sight picture that equate to a group that size...
Bowlers, golfers, gymnasts, baseball pitchers, calligraphers, lots of people do very accurate things without the benefit of "sights" at all.
Look at that baseball pitcher, for example. He's not looking at the ball, nor his hand(s) at all. His "bullet" is swinging on the end of a very long arm that he can't even see. Yet he manages to throw the ball into a very small area. On the other end of that exercise the batter is also virtually blind to his "sights". He swings a bat in three dimensions, without looking, and strikes an object that is not only moving incredibly fast, it's destination area is unknown to that batter.
Nearly every non-drunk, and even some drunks, can, without the benefit of sights or even looking, touch their outstretched arm index fingers together in the classic field sobriety test.
If you can remain relaxed and un-tense, you can close your eyes once you have your pistol on target. The bullet always goes where the gun is pointed, every time. The sights are only there to help you verify where you're pointing it.
Practice seems like a worthwhile exercise..
Sgt Lumpy