Re the first cap. Very nice clean cap.I would agree, it has all the indications to date it to early wartime or even later interwar. I would be extremely happy with it, and you got what you paid for...
However as it is not named, it is near impossible to date it more accurately. It is not unknown for early or late war features to be found different war date period caps. Such is the nature of British caps being private purchase.
Lovely set of photos Michael!