I'm most certainly not an Ascoteer, being Army, but I worked with a lot of Master Aircrew, commisssioned NCA and the odd naughty-boy nav at Upavon for HQ 1Gp MAOTs. One thing I remember is being told it stood for "Air Support Command Overseas Transport". That would seem to tie in with the assertion that UK jobs didn't count.
I don't have a dog in this fight, but that's what the old & bold (and the odd stupid boy) told me. Two in particular stand out. An absolute dinosaur with the initials JM who was ex-Andovers before going rotary, and another ex-Herc guy, Williams of Wales. They both waxed lyrical about their days as Ascoteers. But then again it was 20years ago, and I was but a NIG.