Smith has a great service department that goes out of its way to please its customers. They'll certainly lend you a sympathetic ear. But, your problem is that Smith is very likely to tell you that it no longer has replacement barrels in stock. The 19 was discontinued a couple of decades ago and, in fact, Smith stopped making K frame magnums altogether earlier this decade. I'm not sure what Smith will be able to do for you in light of that.
Sadly, S&W ran out of replacement barrels many years ago, and no more are being manufactured.
Your only real option is to scrounge for a used barrel off an otherwise junk gun. And not to be too pestimistic, but they are very tough to find and if you do, you may have to settle for a different barrel length (which may also mean a shorter or longer ejector rod, depending on your existing barrel length). Check with Numrich, and maybe some big name gunsmiths. And every now and then a barrel might pop up on Gunbroker. It's a long shot, but a 19 is worth it.
OTH, barrels by themselves are so rare that I bet they cost almost as much as a new to you 19.
S&W is now cutting off their warranty work as of guns manufactured on or after either '86, '87 or '89. I don't recall the exact year.
Hopefully, your 19 was made after the cutoff date. I do recall reading a post on THR about a guy who's K Frame .357 cracked the forcing cone and S&W, unable to repair his gun under warranty, offered him a choice of a NIB .357 L Frame (619, 620, x81, x86).
Cracked forcing cones can be a crap shoot. A range down the road from me rents various .357 Mags, including S&W K and L Frames, Ruger GP100s and a Taurus or two. All the guns are 20+ years old, and you are required to shoot their factory ammo when renting. The only one to ever have a problem was the "indestructible" GP100, which blew a huge chunk out of its forcing cone at the 6:00 position. The K-Frames were doing just fine.
Go figure.