Barrel you'd need is this one, currently out of stock
sigsauer.com/barrel-sp2022-357sig.html
But from the QA section of sigs website
"A backorder can be placed by calling into our Customer Service department at 1-603-610-3000 and select option 1. The hours of operation are Monday-Friday 8:30am-5:00pm EST. Mondays tend to have a very high call volume, so please consider calling on a different day if possible, otherwise there may be a wait to speak to a representative."

Chad, I would also check on large gun and accessory sites like (6)un (8)roker, Armslist and Guns America as discontinued and hard to find firearms and accessories show up for sale by private individuals and small shops. Just replace (6) & (8) with G & B.