Hello Chris,
Interesting gun. Is the serial number on the barrel latch the same as on the butt? If it is, it a First Model Safety Hammerless no matter what the serial number says. The barrel was definitely cut and I think not at the factory. I have seen a couple of factory original 1 1/2 inch 32 and 38 Safetys, and one 1 5/8 inch 38. They were special order guns and they had the caliber marked on the side of the barrel. This barrel was obviously cut after it left the factory the first time because the roll markings on the barrel rib are incomplete. The question is did the factory cut the barrel when it was in for some sort of rework. The star usually indicates a return to the factory for some major work. Some private gunsmiths though knew that it was a factory practice to stamp a star and did so them selves when they peformed work on a Smith. The front site is pinned which is how the factory would have done it. Most gunsmiths just brazed it on. The barrel rib also seems to have the slight set back from the end of the barrel as a factory job would have. Again, many gunsmiths just cut the barrel rib flush with the barrel in one cut. The picture quality isn't great, but the milled cut that the site sits in doesn't look right to me. It looks too wide near the base. Maybe I'm seeing it wrong.
In this case a factory letter won't help you unless you know the exact date it was shipped back to the factory and the name of the person who shipped it. That would be the only way to find it in the company records. Without a factory letter to prove it, this is just another cut barreled old Safety even if it was done at the factory. Whoever did it though did a nice job.