You need a .40/10mm slide. The .357 Sig round has the same sized case head.
I thought about building one recently. I've never shot one, nor do I know of anyone who has. I wish I knew more, but I don't have the time to experiment with it. However, I'm not that motivated either.
Winchester 9x23 will deliver the same and maybe slightly better performance with factory rounds. It has low recoil, low flash, and is an ideal length to feed in the 1911 platform. It will also give one more round in the mag.
Of the .357 Sigs I've shot, I have not been impressed with the amount of recoil and muzzle flash. I realize these things are subjective, but shooting .357 Sig out of Springfield XDs and Sigs, I find the .40 version seems to recoil less, contrary to what I read. It makes me wonder what would happen in a 1911.
I would love to hear from those who have shot or own a 1911 in .357 Sig. I'm sure there is someone who loves it, and I'm sure there are very valid reasons why, so I'll stayed tuned to see what others say,