Your reference to the .38-40 as a target cartridge really startled me. I had to do some scrambling to find the .38-40 REMINGTON cartridge, as opposed to the .38-40 Winchester, which achieved popularity from the fact that it could be used both the Colt Single Action Army and the Winchester 73, thus simplifying the ammunition supply problem. The same was true of the .44-40.

You certainly have a fine example of a Hepburn target rifle. The Hepburn was a vast improvement over the rolling block, but shares the rolling block's design quirk making it difficult to create a stock with a high enough comb to shoot comfortably, particularly over long ranges, where the whole range of the target rear sight came into play. This is probably why it was never as popular as some of its contemporary American target rifles, such as the Sharps Borschardt.

I am assuming that yours is a short range model, despite the formidable looking sight.