First off I would drop the 30-378 option off the list. Not really functional in the Rem 700 receivers. It can certainly be built on them, I have built many Rem 700 rifles using this size case but you need extended mag boxes and you should really only use chrome moly receivers because of the increased bolt thrust generated by the larger diameter cases.
The other three will be great choices. For 600 yard and under shooting the 300 RUM is really more then needed but I am never one to be afraid to have more power then you need.
With modern muzzle brakes
, recoil is not an issue so do not let that interfere with your decision unless you are opposed to brakes.
If it were me and I was building the rifle I would go with the RUM but as mentioned, all three will get you what you want and perform extremely well in a top quality barrel.
As mentioned, you need to decide what energy levels you want on target. Also, you need to decide what bullet weights you want to shoot. In the 300 Win Mag I would work best with bullets up to 200 gr and keep impact velocities up there where you want them for good expansion.
The RUM will be able to take any bullet up to the 265 gr class and keep velocities up where they should be for expansion.
This is really not that critical because of your 600 yard range requirements.
Basically, pick one of the three, have it built by an accuracy minded big game rifle smith and you will be happy.
Again, personally I would choose the RUM from your selection but that is just me. but I would not feel undergunned pointing a 300 Win Mag at a bull elk at 600 yards either with the right rifle and load developed for such as task.