Howdy,
A short revolver is hard to shoot well. I use a rest whenever possible, whether that means using a reclining "Creedmoor" style, or grasping a tree trunk and firing across my forearm, or whatever. Further, I have tried the Weaver, isoceles, and traditional one-handed off-hand stances and grips. For me, one-handed is best. I found that my weak hand was influencing the shot and by using only one hand to shoot, I simplified things immensly. Try different shooting stances and see what works best for you.
I hate sights with colored inserts. The darker and less reflective the better. All you want is a dark silhouette in the rear notch. And, focus on that front sight. The eye can only focus on one thing at a time. The front sight should be clear, the rear sight will be slightly fuzzy, and the target will be really fuzzy. Focus on that front sight!
I concur with the other guys about practicing with .44 Specials. Clean the copper fouling from the bore, and your gun will be slow to collect lead when shooting cast bullets.
Unless you have a huge stockpile of jacketed bullets, I would recommend that you give serious thought to a 245-grain Keith SWC in your magnum cases. The SWC has generous bearing surface, and can be ordered to closely fit the groove diameter of your revolver. My best shots have always come with lead.
Ruger uses springs that are more suited to industrial applications than for fine trigger work. Order a set of target springs from Trapper or Wolfe and get that trigger down to 3 pounds. I have a pair of EMF Colt-clones with 1-1/2 pound triggers and it is a beautiful thing to touch one off.
The Redhawk is a great revolver and you should be able to do better than you are doing.
Good luck,
Bitterroot