Well, since it is a 308 now, it has A 0.473" std bolt face and a short mag length…2.8", right? Can it be made 3.0" easily?
Given that, I would be thinking 6 Creedmoor, 6.5 Creedmoor, 260 Rem, etc. Then for throat & twist, you need to ask yourself, what is the ideal bullet and what may I try. If you will shoot mono's, consider going faster twist like 8 twist and then build a dummy round to set the throat.
For barrel contour, if it is a walking rifle, a #3 Brux is about right. For off the bench work, a Brux #5 and up work well. I use the makers name only because their contour chart is pretty standard. Bartlein contours are heavier. To me, the balance point is somewhere around #3 or #4 if much walking will happen.
Length is all about maneuverability and balance to me. In timber, I like shorter, in the open I can go longer like 26". Too long and balance is off. Too short performance suffers. My open country rigs are 28" incl break.
I don't flute. I don't see the value. I know about the stiffness and weight reduction, but it doesn't add up to the price for me.
I don't do carbon either. I'd rather step down a contour to save weight.