MSU, I have hunted with 303 or 30 cals so I understand your feeling. I have a very soft spot for the '06. wonderful at 'normal' hunting ranges.
For me, wind is my biggest enemy. At ranges beyond 300yds, the mid weight 30cal bullets are not very aerodynamic. My solution was to go to the Gibbs. A great fun wildcat (performance similar to the WSM/RSAUM). Unfortunately, still not the best at bucking wind at mod long ranges.
Recently built a 6.5-06 and shoot 140gr SST. WOW, what a difference. hits as hard or harder because the bullets have such a high BC and SD, they simply slow down less. The dents on my gongs are significantly bigger and deeper then with my 30-06 and 165gr SST. Wind drift is about 1/2.
For ranges out to 600yds, I am happier with the 6.5-06. They both have enough energy for deer but if you can't hit the animal, what's the point?
I am now working on a 270 and 150gr SST simply because I want my hunting rifles to use off the shelf cartridges. I will be able to get 270 ammo anywhere in North America. Ballistics should be very similar to the 6.5-06.
If you feel that the 30cal is the way to go, then I would lean towards the WSM or win mag as a min if you want to go to ranges beyond 300yds. With a 178 or 180gr SST or BT, should work very well and buck the wind adequately. The '06 is simply too small to deliver the vel.