It seems to me, that the Win LW would be in the same ball park as a forged Ballard, pressure wise. I bought my LW, chambered in 357 mag and I re-chambered it to 357 Max, long before this forum existed (about 1990). I only had Haas's info to go from so, I didn't hesitate loading it to 357 Mag levels (maybe even more?). Mine is a rebored, original 28" long, 32 barrel, in 20 twist. The bullets that I used are the Lyman 35875 & 357311, both cast 208 gr. I won't say what my GC 311 loads were but, my best 35875 was 14 gr WC820, breech seated, for 1428 fps, I got a little more accuracy with the same charge of 4227 @ ~1400 fps. Primers are still rounded after firing. I always call mine a 38 XL. Remember that if you get the same velocity, using a larger case volume and the same powder, you will always have lower pressures. I think a 357 Max load of 13 - 14 gr of 4227 and a 200 gr bullet, would be safe in a Ballard. Loads of 300 MP will give lower pressures, too. BTW, I think the 357 Max, is one of the very best all round, cartridges!!! It has target accuracy and a lot of knock down power for hunting. In a strong action, you can get 35 Remington velocity's, in a 28" barrel, with fixed ammo.
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