I've had good results with lead alloy in my 45-70, Beartooth Bullets. But they're out of business.
Problem with any lead/lead alloy bullet is going to be velocity relative to BNH. BTB owner came up with a pretty good alloy and they don't deform much, and don't appear to fragment, either - BNH of about 21 or 22. Bullets are .459" diameter, with a 0.37" meplat - they are Wide Flat Nose, Gas Checked. Don't know how many deer and pigs I've killed with them, but I've never recovered one, and the exit hole (other than when I hit shoulder) is never much larger than the entrance. There's nothing other than dangerous game I wouldn't hunt with those, but I'm only pushing them both (425 gr and 525 gr) at a little over 1600 fps; and I'd probably only use them inside about 150 yards.
I'm not sure it would be a good idea with anything in those calibers - even a slow 9.3 or 40 cal is going to be at least 500 fps faster than what I'm shooting out of my 45-70, and 375 will be sneaking up on 1000 fps faster.
Soft lead bullets fired by 45-70 at the original velocities (around 1300 - 1350 fps) in the late 19th century were effective on bison because of a peculiarity of bison anatomy - their lungs are connected, so all you had to do was penetrate deep enough to put a hole in 1 lung and it would cause both lungs to deflate.