Many shotguns now come with a second bead. My Nova has one, my dad's BT-100 trap gun has one... Essentially, make snoman/figure eight (whichever you prefer) and touch the tip of the bird an let the lead fly.
I hear you on the rear sights issue. It takes some getting used too and a long time to master getting that sight picture. Some of my first target competitions wound up with me running out of time on a timed course of fire because I took too long lining up the sight and getting off a perfect trigger squeeze. An alternative to utterly removing the rear sight would be the XS speed dot, if you were interested. Definitely not a bullseye sight but it's faster.
http://www.xssights.com/store/handgun.html
I would prefer a more precise aiming system myself (and since I have already started to get used to attaining sight picture under duress) but to each his own.