Sounds like you are on the right track. There is not much published information about them.

The study of BSA and LSA comercial rifles is a work on its own. The Lee Speed patents were emblazoned upon sporting rifles starting from the days of the Mk.II Lee Metford, intoduced into service in 1892. The commercial rifles were quick to follow built upon that action. They were still available in the BSA catalog post WWI. That opens a wide window, time wise.

Proof markings help to narrow down the date window. Features and options also help.

I am but a student of the Lee Enfield. It is all quite like detective work. I would need to see pics of the rifle overall plus any and all the markings to try to read the clues.

No guarantee that I will be able to date it. There are members of this board much more knowledgeable than me about these. I am wrong as many times as I am right, but I'm willing to have a crack at it.

There is a book on the subject to be published shortly by a member of this board. We await its arrival with great anticipation.