Own a couple of Axis rifles, a 223 (now a 6x45) and a Axis II 6.5 CM heavy barrel. Shooting from bench rest, had crosshair movement on my targets too. Simply put, the stock flexs. In my humble opinion, the culprit for the flex is the weak stock area where rear of trigger guard part mates to the stock. However you use a bipod and I wouldn't be surprised if the fore end of the stock flexs too.
Have a shooting buddy, another retired guy like me, who has bought at least 4 Axis rifles. Two things he does with a new Axis is: work on/adjust the trigger and puts a Boyd wood stock on it. Chuckle, then he'll probably put a better/heavier barrel on it.....he likes the Axis for its action to play with. Me, I'll tweek the trigger too to reduce its pull and then I'll cut out the receiver portion of the plastic stock, flatten its sides, and then build a wood stock around it. Geeeeee, I no longer have a flex problem and my cross hair doesn't move when I'm pulling the trigger.
