Are the mags specific to 357 or are they generic 40/357? I know that Sig marks their mags for both, but Glock 357 mags have different lips than the 40 version. 40 mags generally work fine with 357 rounds, but the non-tapered 40 might not fit in a 357-specific mag.
My guess is that if you can successfully fit the rounds in your existing mags then all you need is a new barrel.