Really depends what you are hunting. On an elk, that should be a killing shot. I think you could lay that paper plate over the vitals and be confident that a shot into that paper plate would kill an elk.
Heres the problem.
Backyard accuracy benchmarks never improve when you throw in unfamiliar distances, angles, obstacles, animal responses, adrenaline, etc. Hold yourself to a much stricter standard than a paper plate if you are trying to determine a max range.
What is really funny is that for so many instinctive shooters around, we sure hear a lot about specific yardages and limits. I personally believe that this sounds nicer than what actually happens. Unless we run around with a rangefinder or hunt extremely familar ground we really won't know the elk is 25 yards instead of our "max" 21 yards as we peer at open vitals through thick brush. Hunting is an art that requires that we aquire a feel for our field accuracy. In the end we go with our gut. All of us pass on shots because they don't feel right.
Here is my answer to your original question. Take the size of the vitals of the animal you intend to kill, divide it by two or three and set that as your goal at any distance. If the animal has vitals of say 12", then your backyard shooting should be at a 4-6" target.
As you learn your effective range, pay special attention to, and be honest with yourself about your first shot of a session and the one shot accuracy you get when stumpshooting. Generally this is quite revealing.