Barrel is floated all the way till the pressure point about half way down this is a normal thing so I here.
I have a couple of T3's including this exact rifle. Both are free floated all the way from the lug forward, no pressure points, nowhere anywhere along the barrel channel where the stock and barrel are touching.
I own two Tikka t3s. Both shoot anything into an inch and a half and several hand loads into a half inch regularly. Both are free-floated and skim bedded at the lug and tang.
JG Raider is right. It should be free floated all the way from the receiver. If you are comfortable removing material touching the barrel, I would do so. If not, I would call Beretta CS and see what they say.
My 2nd guess would be the scope has an issue.
One more thing; I think it was mentioned before, but you can definitely put the wrong screws in the Talleys. I had a guy who brought me a new Tikka claiming it had light primer strikes and would not always fire factory loads... I guess so! He had the wrong screws in the front base and the bolt (hitting the protruding screw) would close enough to let the trigger break, but not enough to completely lock the lugs. Just something to be aware of.
