This is all very interesting to me! I have the same messed up, astigmatism, cross-dominant thing going on. I shoot pistol right-handed, my strong eye is my left.
A while back, I found a new way to aim for me, and it works well. Instead of focusing on the rear sight, which is not easy because of the above reasons, I focus on everything equally poorly! Haha.
Seriously, though, I focus mostly on the target, with both eyes open, head and body square to the target, with no weird tilting of my head. My sight picture then looks sort of like the attached photo. I just had to train myself to know that when it all looks like that, I will hit well. Like I had to memorize that look physically/ optically. I'd say the target is in focus fairly crisply, the front sight about halfway in focus, and the rear sights a little less in focus than that. My right eye (non-dominant in my case) produces a ghosted out image of the whole sight picture that floats up and to the left.
At first, my eyes would fight this and try to pull the front sight back into focus, but now I don't fight it at all, and I can "see" this modified sight picture quickly and easily. My accuracy improved, and shooting is just easier for me this way.
Eddie