Clm,
Here we go taking the thread off topic...
You will need to move up to a Target/DCM/Varmit rilfe as was said. My DCM rifle will do 2" groups easy at 200m if I do my part with my match reloads. You could possibly go cheaper, if you need to, by using a HB 20" and then getting a free float tube. My off the shelf one built by me will do this, but it is not quite as good as the DCM one. It will pull just over 3" at 300m, again with my match reloads.
So, you have options. Which way do you believe that you would like to go? Better yet, post that question as it's own thread so we have it for reference later...
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Yes, 5.56 has higher pressures. I also
believe that the .223 is a tighter chamber. Don't quote me though

-Bidah