I've talked to a few different Sig reps and they all said that the P250 SC .357sig barrel shouldn't be used in the P320. They said that the SC barrels aren't cross platform compatible like other sizes. I found that very odd and even after more questions, they all said to wait for the P320 SC barrel and not buy the P250 one.
I'm the first one to take anything a Sig rep says with a grain of salt. Most of the time you get answers like ... 'well you really shouldn't' or 'I really can't confirm that'. That normally translates into, it will work but the layers won't let me tell you that. This time it was a flat out no.
I have a .40sw SC X-change kit that I already have a 9mm barrel for and am waiting for the 357sig. I much prefer 357sig, but I don't mind waiting. The 9mm makes easy range time