Re:
Another small dating point, are the rectangular style mudguard stay eyes, located some way up their respective tubes.
This was the style in use immediately pre war and up to about 1950.
Later versions incorporate a rounder style eye, into the front and rear dropouts
If you are not happy about paint removal from the underside of the bottom bracket to establish the number, then the steerer tube route is the way to go.
Be prepared for the fact that the stem may well be seized in the steerer tube!
Patience, plus gas, Cider vinegar, Coca Cola have all been successfully employed in the past, so do not be in a hurry
Good luck and look forward to hearing the number and date, Really nice bike
Colin