WM20 2329 was despatched to 'Ministry of Defence, Dublin' in March 1940 alongside a quantity of others. Have you not found an Irish contract for this bike ?
There is no mention of any special finish in the ledgers so the assumption would be that it had a standard MoD finish. I think that I would work on that basis using photo records of Irish contract machines.
What components are listed with the finish codes 3 and 4 ?
I have unearthed all the correspondence between the BSA factory & irish defence procurement dept and the signed contract agreement which my bike is one of - ordered in September/October 1939 & shipped disassembled in crates to Dublin - that is until BSA factory had no wood to pack the remaining 100 bikes which had to be shipped via Holyhead assembled
This in turn created a trade union dispute concerning the lost assembly work - all good reading !
Unlike war dept, these 1940 WM's were not issued with contract numbers/ census on the tanks and were equipped with
Mt110 rear light
Rear seat instead of carrier
Bolt on pillion foot rests
Many supplied with leg shields
Aerolastic seats
Ni fe batteries
The finishes you ask about are BSA combination lever controls mainly & handlebars and I agree with your view - war dept finish is the basis to work on - dull chrome & cadmium & painted handle bars
The shame of chromed levers on the restored machine would be too much to bear
It's often forgotten just how unionised the world was during the 1930s and 1940s and that didn't stop just because there was a war on....and Ireland was a commercial customer of course. There was probably an element of piece-work as well.
There must somewhere have been an agreed specification for the Irish contract bikes and bearing in mind that most of BSA's production for the last six months had been for WD contracts, I'd be surprised if component finish differed.
It may be that the missing control finish codes are simply 'unfinished' and 'special order' or somesuch.
Photographic evidence seems to suggest that some early-war 3SWs had chromed handlebars and controls but then Edward Turner was a showman ! Nevertheless, seventy-five years on, bright chromed levers (whether or not overpainted and showing through)on a dull-finished motorcycle will always look like a post-war botch carried out by the uninitiated or uncaring ! Best steered clear of !
I read with interest your posting on finishes and like you all my literature agreed with yours. However I found an early post-war BSA parts finish which agrees with all those shown in your listing i.e. dull chrome /2 etc., which was followed by Chrome /3. I found similar in a 1950's BSA catalogue.