If your carbine shoots its best with handloads, I would put a good trigger on your rifle and stop right there.....and get started handloading. Shooting an inch with your setup is not to be sneezed at. A carbine in a field configured rifle, and as such, it is doing just fine, with the right ammo, and so are you. The trigger will help a lot, and with that, consistently good ammo, and practice, I think that you should concentrate on producing consistent results.
I have a friend who has a fancy 6.5 Grendal (sp?) with all the bells and whistles. He is a good shot with his bolt actions, most of which have aftermarket barrels, special chambers, and which are loaded for as carefully as is possible. BUT he has had his comeuppance from the AR. It has required that he take an entirely different approach to gun handling to get it to perform.
At first, he thought that it was an equipment issue, combined with finding the magic load. What it has turned out to be is that these rifles are a lot more challenging to shoot small with, even off of the bench, than any of his other rifles. Once he got it through his head that he needed to do what was required for THAT rifle, and not try to shoot it like one of his bolt rifles, he has been able to see some consistent performance.
We tend to focus on equipment, and for rifles that are easy to shoot, shot off of good rests, and benches,there is some justification for this approach, but the rifle that you have is much more demanding. Feed it the good stuff, fit it with a top quality trigger, and practice a lot, thinking about what has worked the best, not just going bang.