The old trick with a broom handle was the way we pulled stanchions up into the top yoke. An old fork nut with the hex flange turned off and a length of threaded bar is a later addition to my kit. That puller is unashamed LUXURY. If you want tools, Cycle Thread taps and dies, 1/4", 5/16"3/8" will cover most of early dismantling and renovation. Threads into Alloy are originally BSW.
If GB2 (we already have a GB) has a shopping list, I'd certainly recommend a repro parts book '49-'53. This will cover the cycle parts, primary transmission and gearbox. The Longstoke engine has major differences in construction from the later motors and does not appear in this parts catalogue. Earlier parts list is available in the Forum Literature section, but includes all BSA models of the year and so is heavy going to find exactly what you want.
A repro bound copy of BSA Service sheets along with a copy of Roy Bacon's BSA Twins Restoration (published in 1986) are another couple of sound purchases.
Things I've noticed. Dynamo terminals are usually at the bottom. The Longstroke engine uses a shorter dynamo drive chain so this may be missing and the dynamo just thrown on.
Be careful with the front wheel. This is the early 7" hub, very different from the later 8" brake with alloy backplate. Likewise Cylinder Head Fins. It is rare to find a head with all the vertical fins intact. Many lose the ones behind the spark plugs when the spanner slips.
"Dinner Plate" rear sprocket, looks to be 49 teeth so bike could have been a sidecar lugger....check for a twisted frame.
Swarfy
Additional. I like the idea of an induction heater for stuck nuts, but I'll wait 'til Aldi do one. Can't justify the present price/use level.