You need to develop realistic expectations for your rifle and it's uses. Tiny groups are great, but a defensive carbine isn't really designed for them. In actual use, you'd be employing the rifle under duress, standing, while driving through a ton of adrenaline. Add in the fact that many of them use a light weight, chromed barrel and a red dot or open sights, and accuracy expectations should be more along the lines of several MOA. If I can repeatably hit an IPSC at 300 while standing, and on the clock at a competition, that's good enough for me. "Minute of man" to a few hundred yards is where a carbine usually belongs. I'm interested in reliability and practical accuracy from my carbines, as opposed to 1/2MOA groups. I have different rifles for that.
Is it possible to build one that'll hold MOA or better? Sure. But it probably won't be very light or handy, aspects of a carbine that I find critical. It boils down to using the right tool for the job, and having realistic expectations of that tool. You're at least half of the equation as well, but be realistic of what your equipment can do.