Yes, Model of 1902 -- and the serial number puts in the First Change category.

I think you called it correctly on the barrel, and there is more evidence that just the apparently modified cut for the older ejector rod knob. If the patent dates weren't missing we could confirm its later manufacture from the last one in the list, but in their absence we can look at the other markings. In 1903/4, I believe the caliber rollmark would be .38 S&W SPECIAL AND US MILITARY CTGS, and it would have been on the left side of the barrel, not the right.

Great shooter. Enjoy it!

EDITED TO ADD: Dwalt weighed in with the caliber marking observation while I was still collecting my thoughts and typing. I can't subscribe to the 1899 suggestion though, for the reasons Guy points out in the next post.

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David Wilson