Are you able to remove the rounds?
When rounds are removed (double check) and you dry fire (it's ok to do) do things operate normally?
You may be experiencing "crimp jump". Light revolver, heavy rounds. As you advance through the cylinder the bullet seperates from the casing a small amount hence not allowing the cylinder to advance. The first two or three rounds may operate ok then by round 4-5 the bullet(s) have essentially lengthened to the point the nose is extended beyond the cylinder.
Are these rounds perhaps reloads? Insufficient crimp?
Solutions don't shoot .357.
Find a lighter .357 round ie. Speer Gold Dot for Short Barrels
In the future you can check rounds by using a Sharpie pen and marking the case/bullet joint and after each round reinspect and see if things are moving. Find a different round.
I carry my 340 with .38spl Plus P SGDFSB. 135 gr.
If this writing is off base call s&W they will pay for shipping both ways and repair for free. You have a lifetime warranty.
Hope this helps.
Definition for "jump crimp" : The unintended, forward movement of a bullet from its original crimped position in the cartridge case. This normally occurs when a fired shot produces enough recoil to dislodge the bullet, which could have been poorly or improperly crimped. Most commonly seen in revolvers and tubular magazine firearms.
OR Lightweight revolvers and heavy loads despite the gun is rated for the round.