I believe that the 500 No2 was a Westley Richards cartridge as they are a standard in their improved martini. A bottle necked round is just perfect for getting around the curve of a martini type action and I feel it was no coincidence that WR developed this round ( I think anyway ) and it being used in their improved action. When they developed this action the 500 3" would have been a very popular round and this would not work in it. To promote the new martini it would have made sense to have a round that gave fairly close ballistics to the 500 3" but allow it to work it their own rifle, hopefully making it a good seller. I have one of these in 500 No2 which I use and I also have a large martini action which I will dig up and compare.
Mine has metford rifling, which is fairly worn, and although I've tried lots of combinations, so far only paper patched bullets and black powder make it shoot well. But then again, it was designed for this combo.
I have at least 1 original round which I will do a drawing of and post.

Underlever