You might want to give the 160-grain Hot Cor a try.
I think that's a good idea. IIRC, Jack O'Connor and his wife used that bullet in their 7x57s with excellent results in Africa. I'd go easy on his load with 4831 though as he was using the old surplus version. Current versions are faster burning so I'm told.
The only cartridge I've shot a 160 gr. Grand Slam in is my .280 Remington. The paper died quite nicely with tight groups as the result. the ones I shot were the older two core version but have not had a chance to try them on game.
Frankly, I think the Grand Slam the old version and the new one just might be a bit too tough for a 7x57.
To quote Jack O'Connor, "Using a 160 gr. Speer bullet in front of 52. grains of No.4831 for a velocity of about 2,260 in a 22 inch barrel my wife has shot elk, black bear, Dall and Stone, sheep, mule deer, and Rocky Mountain goats. Her bag with this combination includes two big bull kudu, roan antelope, several bull sable and about a dozen zebra-mostly with one shot."
I note that he stated the 160 gr. Speer but didn't say they were Grand Slams. In several other of his books, he mentions the load but never mentions the Grand Slam. He did at least part of the time say he was shooting Nosler Partitions in some of his cartridges but again not in the 7x57. Does leave one guessing as to what he really used at times in the 7x57. About the only commercial 139 gr. bullet I can think of is Hornady's and he did like 139 gr. bullets for deer and the like.
I've been getting some interesting results with the 150 gr. Nosler Partition and Rl17 powder. I also have a fair amount of 160 gr. Speers, both Hot Core and Grand Slams so I just might try and duplicate Jack's old pet load.
Paul B.