When I guided in Maine I had several guys show up for the moose hunt with the bigger Weatherby's. The 300 was most common but a few with the 30-378,338-378,and even one with an older 375.
I loved to see this as there was minimal or no tracking. I had a "sport" kill a moose using a 270 Wby Mag across a clearcut at a lasered 590yds.
I cannot remember the bullets used. Most Wby shooters used handloads as I remember. With the extreme speed produced it is not advised to use the run of the mill 30-06 bullets.
I believe the no lead bullets would be great for these guns. No jacket to shed but there would be a possibility of petal seperation. --- SAWMAN