The 6.5 C should be a great choice.What I wanted to suggest about the original question:Consider percentages.
I am going to make some rash seat of the pants statements about ranges.They are for visualization purposes only.If you don't agree with them,fine,change them.The number does not matter.
Suppose the 257 R is a 300 yd clean kill cartridge on a deer.Suppose the .264 stretches that to as far as the shooter can gage wind,range,mirage,etc.Call it 600 yds.
What percentage of real world deer hunting shots will be between 300 and 600 yds?What percentage will be 300 yds or less?
The 264 has advantage on the over 300 yd shots.
At 200 yds,a more common hunting shot,the 257 shooter has been practicing with a mild rifle.It is easy to shoot well.Bang,thud,dead deer.
At 200 yds,if a magnum shooter keeps his eyes open,Bang,Whap!Dead deer.
Now,go dress it and cut it up.You will get more good table meat with the 257.
IMHO,there is a value in the 90% shot rifle.Sometimes,you may have to get closer or pass the shot.If you carry the 10% specialized rifle,it still does not guarantee shot placement at 600 yds,but its always heavier,messes up more meat,kicks harder,makes more noise,and burns bbls faster.
A long time ago,I bought an old round,40's Ford sedan looking 63 Volvo 544 for $400.I drove it 13 years before I gave it away,still running.It got 30 mpg on the road,was dependable,would break any speed limit,etc.The 257 Roberts is kind of like that old Volvo.