I agree with James, but another method that works with the captive extractor is seating the bullet into the lands and using a mild (not max load) fireforming the brass. This is similar to the JDJ method of fireforming brass.
My friend has a Encore from JDJones at SSK Industries in a .338 JDJ and he uses 35 Whelen brass to form his brass. He makes a False shoulder, by necking down, to head space off of then fire forming and had excellent results with this. I know that this would be tough with a .223 Rem, but a 6mm/.223 Die could be used to neck up then re- neck down to do this same method with a Gibbs Style Chamber.
Another Alternative is to sell the exhisting bbl and get a premium after market bbl from Eabco, Bullberry, or SSK there are others that make high quality bbls, but I've had experience with with those others and would put Eabco on the top of the list.
If you could get enough out of the old bbl, the cost of re-chambering your exhisting bbl would be pretty close to the final cost on the custom bbl. Those guys also guarantee the accuracy of their bbls.
Dan