The first answer is that I do not know if you would have to change bolts or if your bolt is close enough to work with the slightly different head diameter.
But, from a practical dollar standpoint you are probably better of selling your 6.8 Police model and purchasing a different rifle. There seems to be a small number or people who are really into the 6.8 and chances are you could sell your rifle and purchase one in a caliber that you desire for less than a rebarrel.
With that being said, should you decide to rebarrel, Pac-Nor offers a rebarreling service that includes truing the action, fitting and chambering the barrel, and the barrel for right around $500. A friend has had two Remingtons done by them and they both are 1/2" shooters with sporter weight barrels. I was impressed by the dollar value of the service and the quality of workmanship. If I recall the turn-around time was about 3 months.