Thanks again for the suggestions everybody. We're now leaning towards Aberdeen to Manchester, then Manchester to Singapore. There is a 3 hour layover in Manchester which is not bad. We missed the option before as the Manchester flight wasn't running on the dates we were looking at originally, but comments here made us look again. I don't realise that flight isn't daily.

Pricing is still a premium, but the Loganair transfer flights are much more reasonable than KLM.

Thanks again everyone.