I have a couple of thoughts for you about the origin of the single threaded hole in the bottom rib of your Henry DR. There are two phases of screw thread sizes and thread pitch in vintage UK guns and rifles. Phase one is prior to about 1900 when the UK gunmakers largely made their own screw taps and dies and there was mostly no standard thread sizes in the gun trade; and secondly after 1903 when the BA thread size was adapted although it was introduced in 1884. Your rifle made in 1875 had screws made peculiar to the Henry shop one expects.
If you find that the threaded hole in the bottom rib fits a standard thread size of today whether BA or some other thread pitch then the thread age is suspect. If the threaded hole is not a modern day thread pitch examine the number of threads in the bottom rib of the threaded hole and if the threads are more than 4 then Henry may have made the bottom rib thick for the addition of a sling eyelet. A typical bottom rib usually is only thick enough for about 2 threads maybe 2 1/2 threads.
You may want to procure a double loop English style shotgun sling such as this one:
https://www.franken-cie.com/Shotgun-sling.htm?websale8=franken-cie.English&pi=1-4070