The throat in your Remington 700 sounds familiar as I have couple with long throats as well. What is the overall cartridge length with the Nosler BT? Curious how much difference between col and magazine box length. Sometimes rifles like a lot of bullet jump, sometimes not. Depends on the rifle...
My son uses 30-06 brass necked up to 338-06. I'd recommend annealing before necking up. Will help with longer case life in regard to the necks. Good idea to try to keep a little better track of your cases as to number of firings. Let us know how it works out for you.