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@clubman I take different approaches depending on whether it is a cycle that gets used regularly and put away wet or brought out on sunny Sunday afternoons for ceremonial purposes. The first is whatever works well and doesn’t look too bad. The second is trying to match the original to the maximum extent possible.
After all, any old bike in regular use over decades has had worn components replaced, usually by anachronistic items. Its components reflects its own history. My bike custom-built for PBP99 and used for lots of long brevets since has had almost every component changed over the last quarter century.
If you want to keep using cottered cranks and you can’t find Chater-Lea bottom brackets components anymore, your best option is to sleeve the bottom bracket like the Tandem Club used to do, letting you use easily available BSA-threaded BB cups and cottered axles.
LWaB-
I don't think there's any disagreement between us. My bikes are in your first category - I don't happen to have any that are 'ceremonial' only. I do have a wet weather bike - the rest I prefer to keep dry.
It's worth noting that very few old lightweights advertised for sale have their original components, just like your PBP bike they've been used and had replacements. Back in the day any sensible clubman would have chucked away that original Benelux and replaced it with a Campag as soon as he could afford it! Roadsters are a different proposition since the owners usually weren't enthusiasts
It's pleasing not to go too far away from the original kit, and so I would certainly prefer to use cottered cranks on an old frame like that Saxon. It's good to hear of these methods to overcome problems, but also it's just as well that potential buyers know what they are letting themselves in for.
clubman
Chater Bottom Brackets
Those Phil Wood adapters look like the answer - as long as you want to use a modern sealed bearing, which I guess would exclude the use of cottered cranks. My bikes certainly have anachronisms, but not everyone else is so liberal about this and I think it's true to say that square taper cranks would be anachronistic on any frame with a Chater BB.
If you want to use cottered cranks, I think you will still need a Chater spindle as well as the cups and the 5/16th balls. In the photo below you will note that the Chater spindle (top) has narrower shoulders than the other one (TDC) which is the standard ancient British size and which, incidentally, is interchangeable with TA and Stronglight.