Condition: Perfect as in no wind. Accurate range determination.
Range: 400 to 700 yds
Cartridge: 338 RUM, 225 Hornady Interlock @ 3090 FPS MV.
Enviornment: Very steep mountain sides, shooting across canyon etc.
Part one: where would you put the bullet?
Part two: If bullet were Nosler 250gr Partition @ 3050 MV where would you put the bullet?
I may be the slowest guy on the mountain . . . . but . . . . I'm on the mountain!
I'd line up my vertical cross hair with his front leg and hold the horizontal line about 1/3 -1/2 the way up from his belly. The shock from the bullet will likely break the on side shoulder , take out both lungs possibly the heart. At that range the report woulden't spook him that bad so if he does take off with a probable broke leg he won't go far with to shot out lungs.The partition would pass clean through leaving a good exit. The Interlock would likly pass through also unless you did hit the on side shoulder then still I feel that this bullet would at least make it through the lungs.
Why not shoot the Accubond ??
Also don't over look the 338 cal Ballistic tips as the 338's are built a good big stronger than the smaller cals.
At the ranges you list I'd go for the shots on the pic below. Don't know if you have this pic but it also shows the organs and muscle locations. A heart shot is not one I'd look for at 700 yards but I know the high shoulder and the #2 placement have worked on a dozen or more so I'll probably keep on plunking them where it seems to give me the best results. Elk are a big tough animal, but they have a very adverse reaction to a properly constructed bullet placed in the right spot. They have a tendency to die, especially if they are in a totally relaxed state when you make the shot.
If you are gonna have to pack him up out of the canyon if he doesn't drop at the shot then I'd say to break him down. I've spent all day packing big bulls out of deep canyons and I don't want to have to do that again.
I agree with your #1 shot location almost exclusively. It is my shot of choice. Being in line with the spine as far as elevation it also allows for a fair amount of windage that seems to be the plague of the long range hunter. Given that I prefer this shot placement I pick bullet and cartridge combos that work accurately and penetrate deeply, a bullet that expands is a safety measure for times when the shot slips into the lung area.