If the cartridge shown above is the proper one for the rifle, it is neither 577 Snider nor 577- 3 1/4". Rather, it is 577- 2 3/4", it seems the confusion results from measuring the overall length instead of the case length to arrive at the longer designation. The idea that 577 Snider may have been the original chambering has at least, some merit. Cape guns bound for South Africa were very often chambered for the military cartridge at the time, which would be available for issue if the owner were "called up" for service. After the service cartridge changed to 577/450, the owner may have decided to rechamber to a more powerful cartridge, or a subsequent owner may have. This is speculation based upon reasonable assumptions.
Mike
