1911's seem to do just fine with hot rod 38 Super IPSC loads, the 357 Sig doesn't come close to what those guys shoot. Recoil will beat a 1911 up more than pressure and the 357 sig isn't going to recoil more than a hot 38 Super or 9x23.
Winchesters load data shows standard pressure 9mm up to 32,900 psi, they list the 357 Sig at 33,000. If pressure was the problem the 1911 wouldn't hold up to the 9mm either.
It may well end up being cheaper to just buy a new gun chambered for the 357 Sig than to try to convert your 1911, but it seems most custom things people do to handguns are based on "want" rather than what's practical.