I have a 3" M60 from the 80's that also won't let jacketed .357" bullets drop through the throats. The few .355/.356" bullets that I have experimented with didn't shoot very accurately. I personally don't think you will harm your revolver with .357" jacketed bullets loaded to reasonable pressures as that is what it was made for.
Having said that though, swaged or cast bullets should be easier on the old girl, and shooting slightly over size lead bullets is not going to stress anything.
I would enjoy shooting the gun, keep any +P loads to a minimum, and not worry too much about it.
