I visited the Scotland's People centre today and was finally able to work out the answer to this mystery. It's simple, in a sort of maddening way ... and it makes me feel a bit bad for wasting some of your time, but I just didn't know the circumstances and neither did my mum.
Charles Duncan Gray was born in 1915; I found his birth cert. and confirmed that he was the right man with the right parents. So far, so good, but still mysterious.
I then learned that his father died in 1916, as did his only sibling (I didn't even know about her until today; she was only 13 months at the time of her death, and Chick was about 2 months old). His mother Catherine went on to remarry in 1924. We had been aware she remarried, but had struggled to find the evidence, and believed it to have happened considerably later, after Chick was an adult. It looks as if the young Charles took his stepfather's surname, becoming Charles Duncan Powrie -- at least, that is the name under which he is recorded as presumed dead in 1940 whilst engaged in "air operations". It was (unsurprisingly) easy to find once we knew about the surname change.
He is commemorated on the Runnymede Memorial in Surrey. I'm so, so pleased to know this and hope it may be at least mildly interesting to anyone who was kind enough to post on this thread earlier. Thanks again -- the information and tips you provided have been useful and interesting, despite the fact I had you barking up the wrong tree on my behalf (sorry again).