John B 45, Put down the crack pipe & step away from the computer. I am glad you picked me for an example.
The scenerio you present gives no advantage to the 25-06. First problem I see is you want to drag a camera man along on a trophy bull hunt. Have him stay in camp & head the oppisite direction as you in the morning. He can film bulls & cows a few miles away from where you are hunting. You can take him with you after you kill a bull & get some good fotage of the dead bull. Take your camera man out & stage several scenes after you have killed your bull. This will take at least one extra day? Make it look like you are hunting. Change your clothes a few times. People will think you are filming this for several days while you are hunting. A few days in the editing room & you have a hunting show with you killing your trophy bull on it.

Lets address the rifle probelm. Your load of choice for the 25-06 uses a Hollow Point Boat Tail bullet. This is a paper or varmit bullet. Your load of choice has a muzzle velocity of 3100-f.p.s. this delivers less than 1300-foot pounds of energy @ 400-yards.
I would work up a load with a premium bullet & put this rifle back in the safe. The 25-06 is a deer rifle not a elk rifle.

The 375-R.U.M. with a 260-grain Accubond is a good quality bullet that will stay together with any shot at any angle. The 375 with a muzzle velocity of 3100-f.p.s. has about 3300-foot pounds of energy @ 400-yards.

The 375 has more energy at 400-yards than the 25-06 has at the muzzle. The 25-06 at the muzzle will deliver about 2500-foot pounds of energy.

The groups you listed were no better with the 25-06 than the 375-R.U.M. I am going to need a solid rest at 400-yards with any rifle regardless of caliber. In fact 400-yards is too far for me to shoot unless everything is perfect. If I had the time & cover to work with? I would close the distance to 300-yards or less. Closer is better. Closer gives me less chance for error regardless of rifle or caliber.

If this hunt was for real & I had to pick my gun right now? I would take my 300-win mag loaded with 200-grain Nosler Partitions. I have killed several elk with this rifle. I know what this rifle can & will do. This rifle has been at my side for close to 20-years. Give me a few years with the 375-R.U.M. & I might pick it over the 300-win mag?

The 375-R.U.M. is more of a toy for me. I know I will never need the extra power the 375 offers. I wanted to play with a big mid-bore for a few years. When I get tired of the extra recoil I will sell it.
I can promise you one thing. I will not take up elk hunting with my 25-06.