Yes the 600 Rem can be rebarreled.....and if it needs a new barrel, rebarreling to the 6.5 Rem Mag is a great idea.....The 6.5 Rem Mag is a great cartridge and the 600 Rem rifle makes it a special gun.
Personally, I'd use a Shilen #1 contour or a #2 at the heaviest and a 20" or 22" barrel...It's your gun so choose the length you like...
I strongly recommend choosing barrel length for your carrying desires and not for some preconceived velocity advantage. Have it your way!!!