Aside from the parts needed, which is a straight forward technical matter, I have to wonder why go with a .357 Sig in a "1911"??
My curiosity about the choice is because of the way I look at things, which isn't always bottom $ driving my choices, nor am I constrained by "practical" necessity.
Unless otherwise specified, to me a "1911" refers to the full size (5") Govt Model gun. So now I'm left wondering why the .357 Sig? If tis round count, other guns offer more. If its the power of the round getting you into "real .357" country, and you're looking at a full size gun, that makes me wonder, if its the power you're after, why not go with a real .357?
There is one very close to the 1911Govt model, in both size and design, the Coonan.
The Coonan I have is 1/4" longer, 1/3" taller and 1/4" thicker than my Colt Govt model .45acp.
For me, that just enough of a difference that you notice it is slightly bigger, but not enough to matter in any practical way. THe advantages are the ability to shoot full .357 loads, jacketed or lead, and the gun can be converted to shoot .38 Special as well.
Downside? rare, oddball, not easy to get and of course $$$.
The other .357 semi auto pistols are significantly bigger and heavier. But if you want FULL .357 power, they are currently, the only options.
The LAR Grizzly in .357 Magnum is a "real" 1911 design, though stretched and beefed up at points. Some standard 1911 parts can be used. WHEN found it can be either a 5" or 6" which give very good velocity figures.
Sadly, the LAR Grizzly is long out of production, so getting one isn't easy (or cheap).
The Desert Eagle in .357 is a real beast. HUGE and HEAVY, but accurate, low recoil, and will handle the hottest JACKETED bullet loads. Downside, besides the size and weight are the trigger isn't quite as good as a 1911 can be, and you cannot use lead bullets and the gun isn't "adjustable" to ligher loads.
IF you are impressed by a .357 Sig making 1450fps with a 125gr from a 5" I would expect a 5" Coonan or Grizzly in .357 to deliver a bit more, and I know that my 6" Desert Eagle will take a 125gr JHP past 1700fps, as I've done it.
There's no free lunch, so what is the object, to get the most power "practical" from a 1911 pattern, and size gun (practical by your personal standards), or getting the .357 power from a semi auto pistol?