I'm a relatively serious (as in I work to be as good as I can be) and decent enough (A class) USPSA Carry Optics competitor. None of my match pistols have sights that are tall enough to see through the glass. I have zero trouble drawing to any target, no matter how awkward it is, and having the dot show up on target.
How did I do that? Through thoughtful, honest self critique of my draw and by fixing it through disciplined dry fire.
You need to abandon the derp idea that you're going to use the BUIS to find the dot when it doesn't immediately appear at the end of the draw. You need to fix your draw and your index until the dot appears where you look 100% of the time freestyle, strong hand, and weak hand. If you won't commit to that, just take off the dot and sell it because you'll never realize its potential.
What if the dot dies? Have you ever tried shooting with it off? I have and what I found is that I can make guaranteed A zone hits at up to 10 yards running .3 splits, and out to 15 yards running .4 to .45 splits by framing the target in the empty window of the sight. I have shot out to 30 yards that way to see what would happen and accuracy falls off quick past 15. I'm ok with that. Id have a hard time justifying a self defense shooting that far away. In any case, using quality sights (Trijicon) means that the issue is even less likely than me needing to shoot someone. One caveat, this works well only if your grip and your index (index meaning the pistol goes to where you look without having to refer to any sights) are sorted out. IMO, index is just as much of a fundamental skill as a clean trigger press and a grip that lets the pistol recoil controllably and repeatably.
Only one of my pistols has BUIS and that's because I didn't know better 2 years ago. They're likely coming off.
And stop trying focus on the dot itself.