We know that the most famous Birmingham maker of all, Westley Richards, had what few best Sle guns made for them by AA Brown.
So, the most famous of all, could not complete their best Sle gun.
We know that WR made some of the finest guns in the world, both shotguns and double rifles, of course they could make SLE's if they wanted to. Just because they didn't make them does not mean thay couldn't make them. Perhaps their own best craftsmen concentrated on their best BLE's and drop locks, and the small numbers of SLE's ordered would have meant that customers had to wait longer (perhaps too long) to get their guns? The easiest and fastest way was of course to order finished guns from the Birmingham trade.