I only shot my Contender in 44 Mag at an indoor range one time: The blast drove 2 other people out of the section of shooting bays I was in and after only half a dozen shots (25 yards) one of the store workers popped in to ask what in the heck I was firing. I guess the full-throttle Contender loads made him a little nervous because he asked me to try some of their reloads that were quite a bit milder. I never shot it indoors again because I had a vicious headache later that day. I could feel the concussion from the sound bouncing back and hitting me in the head, with my handloads. The store's reloads weren't nearly as bad, but from then on, I shot it outside.
I hope I don't offend you by saying this, but I think you would be best served with either a fixed power scope of 2 or 4 power magnification, or a 2X - 6X variable. I don't like "dot" scopes or holosights on guns like the 44 Mag. With the barrel you have, and a good scope, you could shoot the group you described at 50, 75, maybe even 100 yards, with some practice! Not feet; YARDS! That's an absolutely beautiful hunting handgun and as such, you really need a scope with some magnification to take full advantage of it. My 44 came with a 2.5X T/C scope and was upgraded to a 2X-6X LER Bushnell. I shot 12 rounds one afternoon, in groups of 3, at a 50 yard target. When I walked downrange to check my group, you could have covered them all with a coffee cup! I'm not a great shot, but that gun sure does shoot great.
Since then, I've had a short barrel extension added, making the barrel 16.5", so I can mount a buttstock and shoot it as a carbine. This was done because of Indiana's dumb gun laws. At the same time, I switched to a 2X-7X standard eye-relief scope and the groups are better than ever. I hunted with it last fall and came very close to harvesting a fat doe with it, but the wind was swirling and she just wouldn't come that last 20 yards, to clear the brush she was hiding behind.
My advice is to put a scope with some magnification on that bad boy, forget about shooting it off-hand very much and take it out in the woods this fall. That's what it's made for and anything less...well, you might as well shoot 9mm or 38 and save yourself the cost and headaches.