Actually, the picture was copyrighted by C.S. Fly in Tombstone, AZ in 1886.
I can't find any provenance beyond northern Mexico for it. The vegetation in the image does match that for the Chihuahuan desert (which does include southern New Mexico)and for Skeleton Canyon where his surrendered in AZ.
In 1876, he surrendered and did have a Winchester 1876. At his surrender in 1877, he was using a Springfield trapdoor.
While repeaters may have been around, it doesn't necessarily mean that they would have been what he was carrying at any given time. Keep in mind that repeaters had been a round for quite a while before Custer and his group were killed at Little Bighorn and they didn't have repeaters.
I definitely think those are cartridge belts. Do you have another explanation for what they are?