I can add add a fair bit to this list, based on my Barr and Stroud data.
Donaldson & Kelso became Knightswood Motors in Anniesland and built the Royal Scot. Actually, they built a few.
The Motor Mart in Edinburgh bought two engines, so I assume built two bikes.
New Gerrard, of course.
William Oliver of Jedburgh bought one engine and may have built a single machine.
North British Machine Company in Glasgow bought a few engines.
Collars Ltd in Anniesland bought a couple of engines too.
Wallace bought a few. Whilst they were more known for agricultural equipment and have no record of producing motorcycles, the few B&S engines discovered in the US were sold through them.
There was also a McKechnie (Edinburgh) entered in the Scottish Six Days in 1922. Retired on day 6.
Any B&S information, extant engines etc, welcome.
JFerg