30 cal brass brush works just fine with a 223 case (perfect size to pull back into the split case so the bristles are the a good angle to get a good bite on the inside of the case).
Note, for 308 split cases, I use a 45 cal brass brush instead.
Single one piece cleaning rod, drop it down the muzzle until the end of the cleaning rod is out the back of the receiver, install a 30 cal brass brush on the cleaning rod, pull the cleaning rod back into the case until you have the brass brush up against the case neck (brass bristles now angled toward the back of the receiver in the case to get a good bite on the inside walls of the split case, then give the handle of the cleaning brush a hard blow to drove the rod/bush/split case out the the chamber/ back of the receiver.
As for the brass brush now stuck inside the case, it's pretty much toasted at this point (plus a PITA to get out of the split case), so i just end up spinning the brush and split case off the cleaning rod, and throwing the two away.
Note: split case extractor works well too, but since I always have a single piece cleaning rod with me (in the gun case) as well as extra cleaning brushes in my carry case (223 through 45 in the case as well), it just easy to use the cleaning brush and brush, instead of having to lug a bunch of split case extractors that are caliber specific instead.