I did some more research and disassembled a similar quality Australian rook rifle on a smaller sized small Martini framed action. Marked by a large Australian gunsmither and seller, but I believe the action was a trade action my Tranter. It appears to have been marked the same way with the barrel proofed in Birmingham.
I also did some research on Stevens barrel sizes.My best guess now is that you are correct and it was a nice grade of english rifle that found it's way to the US and was rebarreled with a Stevens factory barrel.
The barrel is marked as "1" and the dimensions of it's profile match numbers I found for a Steven's number 1 barrel. It is exactly 26" in length and the octagon section is 9" long. This would agree with cutting 2" off a 28" No. 1 profile barrel, rethreading and rechambering back to the original cartridge of the barrel. The Stevens tenon is way too long and complicated (and small) to fit in the action. The id of the tenon at the chamber exactly matches the max circlular dimension that could be obtained from the octagon barrel section.
Also, it would be rare to find an English gun of much quality to have an octagon barrel during this period. I suspect the fore end was fitted to the octagon section as part of rebarreling. The J.A. stamped inside the barrel channel may be the mark of the gunsmith.
The whole rebarreling would not have been a quick job, what with cutting the barrel, with only the barest minimum of metal available, then indexing the barrel to exactly the desired length and redoing the fore end.
It's a nice rifle and since probably no real collector's value, I will likely clean it up, refresh the stock and hopefully have some fun shooting it. As an aside, it is the smallest small frame martini I have ever seen (hope that's not confusing). I suspect it was originally a Rook caliber similar to the Australian one I have. At the price I paid for it, the action and stock work are a bargain at the price I paid.