Hey, Kakali:
Two of your three options are wildcats to begin with...so let's go wildcattin!
I have a 25-06 Ruger Mark 1 which is a death ray with 75 grain VM's, and I go with the others on saying the advantage is factory ammo.
However, I sometimes think about going to a 257 Roberts Ackley for the sort of shooting I do with it. My dad and a crony both have 257s and when they blow stuff up, their stuff blows up just as much as mine, on less powder.
If you insist on going to a 6-based cat...perhaps the best option there would be the 243 Ackley Imp or 6MM International in order to balance your bore with powder capacity.
If you want to go loudenboomer wildcat 6.5 so you can get all those funny-looking long 6.5 bullets that make 1000-yard shooters smile in their sleep, then keeping the basic 06 case, either off 270 or 2506 brass, again, that should be a good, balanced cartridge. Maybe Ackley the shoulder just for fun.
A WSM 6.5 might be pretty good, but on a Parker Mauser (oooh, I'm jealous) the feed rails might demand modification.
Finally, on the 6.5-06, you could always shorten and rechamber to a "6.5 Roberts Ackley Kakali Special" or just plain old Swede if you so desire after having to wait too long between shots...
Gee, ain't this fun?

Up hills slow,
Down hills fast
Tonnage first and
Safety last.