Higbean started my thought---once you start shooting your groups, put the cleaning rod away. You'll probably get one flyer per group when you clean in between groups.
But there's so much you didn't say that it hard to give a good answer. Does the barrel free float or does it use a pressure point?, does the barrel contact the stock on the sides of the barrel?, are you pushing on the rifle while shooting?, breathing right?, what are you using as your rifle rest?, how heavy is your trigger pull?, how long between shots?, the list goes on and on. What do the groups look like? Unless you have a gauge, put the base of the bullet at about the start of the neck, unless this makes your overall length too long. Later you can fine tune by adjusting bullet seating. Is this the only gun your shooting? Take along your 22LR and practice about 50 shots with it to get good groups before moving up to the 223.
