I've just checked the submissions requirements for BeWrite at bewrite.com and they want double quotations for speech and single for all else, so maybe they are American based.
Is there an easy way to swap them round using find/replace in Word without making a dog's dinner of it? All I can think of is transferring one set into third party symbols, swapping the second set round, then going back and altering the symbols.

That's the method I'd use. But I don't see using double quotations for speech to be so "American", as that's the style I've always used myself.

Perhaps the result of reading too many American books?