A .223 Wylde Chamber is the same as .223 Remington, lead/throat is longer for heavier bullets. Assuming your dimensions are correct your chamber is .008 too short. Most virgin brass is .003-.004 shorter than min. chamber. If the rifle was mine it would go back and get chambered correctly. If your continue to force the bolt closed on tight brass you can gall the locking lugs.
John
SAAMI actually allows brass to be 0.003" longer than chamber if one chooses. As long as dissimilar hardness and/or lubricating lugs, you won't get any detrimental galling from normal pressures.
There's plenty of people who prefer there to be resistance when chambering. I'm not one of them, but can't deny that plenty do this without any detrimental issues.