What a lovely little bicycle with a nice history that I hope you can find out more of.
I do like bicycles that may have had upgrades by various owners as new technologies became available.
As to Bayliss-Wiley, they were established in 1919 before being bought out by 'Perry and Co.' in 1926.
It remained part of the part of the parent company, 'Perry and Co. (Holdings) Ltd and was, I believe, still part of that company when it merged with 'Renold Chains' in 1959.
Interestingly, they had an overseas selling and distribution operation in New York from 1948 up until the mid 1960's, marketing all of the groups products.
So perhaps they were producing 36 hole hubs for the US market during this time period as the export economy was so important to British industries.
They also had similar selling and distribution of
operations in Belgium and Canada (both closed in '64) so I think it's not unreasonable to assume they produced lots of their hubs with 36 holes, as Belgium would also have used this configuration, so perhaps you could consider 1948 onwards as a date for that hub?
The fixed and 3-speed hub was very popular in France during the 1930's/40's and continued into the 1950's.
They were also popular in the UK, but as has been stated above, usually in the 40 hole configuration.
As to a more suitable derailleur, the early ("double cable") Cyclo models may be more appropriate, the 'Standard' or 'Oppy' models from 1948.....
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as would their early single cable models such as the 'Super Olympic' (above) or, if one moved forward a couple of years to a date of 1950, you could consider a first generation 'Benelux' model.....
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...and of course if you stayed with a French option, there are so many that may be suitable.
Personally, I would stick with what you already have, as this is how someone decided to enjoy it a long time ago, but that decision is yours.
(Images from the excellent 'Disraeli Gears' website)
“You know how the title came about - Disraeli Gears - yeah? We had this Austin Westminster, and Mick Turner was one of the roadies who’d been with me a long time, and he was driving along and Eric (Clapton) was talking about getting a racing bicycle. Mick, driving, went ‘Oh yeah - Disraeli...