I say shoot the way you want, back in the early 70's many people shot with sights.
My question would be is at 15-20 yds. what is happening when you shoot without sights ?
Burch says his windage is bad, if so, why ?, there is a reason for it at short distances. I could understand that you take a 35-50 yd. shot and are wide left or right but not at 15-20 yds.
I have friends that should shoot very well yet they don't, but it's for a reason that can be corrected. have you guys tried getting some lessons ? or take a video of yourselves shooting and post it up here, I am sure the Trad family could help you out.
Again, do whatever you want to do, I just feel that it might be at your finger tips and for some reason it's escaping you.
Good luck whatever you do.