I ended up in your same predicament with 3,000 Remington 6-1/2 primers. So I did a little research and found this article by James Calhoon. According to Mr. Calhoon as long as your stay below 55,000 psi the Remington 6-1/2 primers will be just fine and since he classifies the the CCI-400 in the same class, which is the primer I have always used for my AR without any issue I have have no reservation using the Remington 6-1/2 primers. His chart in the article shows all the critical dimensions for CCI, Federal, Remington and Winchester. So unless you are using some off the wall hot load the Remington 6-1/2 primers will be just fine in your 223.