For all practical purposes the 5.56 and the 223 cases are identical. It is the pressures to which they are loaded which makes shooting 5.56 in a 223 chamber problemmatic. You can use milsurp cases in your 223 loadings. Run a few through your sizing die and trim to length and then weigh them. You will find after weighing maybe 20 or so that there is a weight range. I make 3 piles, one lighter than the range, one heavier than the weight range and the vast majority within about 2 grains of each other in the middle.
I toss or sell the heavies, and work up loads in the big, middle +/- 2 grain pile, and then use the light ones for 200 yard loads or less.
Oddly enough they all seem to shoot pretty darn good. Just cull the heavies.