I have 2 .257's one a Lazermark the other an Ultralghtwght.
I shoot 115 Baltips over H-1000 I have used this load to take very large caribou 337yrds (shot broke shoulder, spine and opposite shoulder) but some would say the bullet failed 'cause I only found the jacket under the skin on the off shoulder. Antelope beyond 500 and whitetails at close as 30 yards without alot of damage. Nosler has perfected the jacket on that 115 for use in the Weatherby and it shoots 3 shots under an inch at 200.
The Lazermark I shoot 100 TTTSX's over Magnum. It was re-barreled with a 26" #2 by Weatherby as I shot out the 24" #1 I had been using 100 Sierra's over RL-22.
A good 120 load is the Speer over IMR-4831
This is a high intensity cartridge and generates alot of heat fast. Let the barrel go cold, I mean cold before shooting another group. I shoot 3 shot groups in under 60 sec. why you say...think hunting conditions...1st cold bore shot count period. Never needed a follow-up....but good to know how rifle will respond if needed in a hunting condition.
You should find COAL to shoot best about 3.305 to 3.330... oops that's for my Weatherby's except for the TTSX's