For the hunting techinque you describe I would (and I did) go with a full competition action. Nesika is good
For that type of shooting you should just go with a single shot. Nesika has actions ready to ship often times, so there is no wait.
As far as caliber goes, I am not going to argure with the 338 people. I will simply say that a 7mm Allen Mag and a 30-378 are reasonable alternatives with good kiling ability to 1500 yards. I have not killed an elk at 1500 yards with the 7mm AM but the gear is being assembled and the drop data is being compiled. Finding a cooperative elk will be a problem I suspect. There may be 30 caliber wildcats similiar to the 30-378 but I do not keep track of them.
If you like laminated thumbhole stocks and want something special for a different kind of long range rifle contact Joel Russo of this forum. He will laminate the layers in your choice of colors and then will shape the forened to meet your preferences in width and shape and lenght.
Barrel lenght would depend on how radical the cartridge is. Most people use a 28- 30 inch barrel in such a rifle. I use a 34 inch barrel.