Ian, just adding to the already given great advice. Since the carbon builds up on the inside, I find that it helps on really stubborn ones to split the manifolds so that you can get at the flapper from the inside. Use a small screwdriver to scrape away all of the carbon deposits around the shaft. Get down to bare metal. Then apply the Kroil to both the inside and the outside where the shaft goes through the manifold and do the tapping.
As stated, persistence and patience pays off. Spray and tap a few times a day. I have had them take over a week to break loose, but they always do.
And as Martin stated, give both sides a generous shot of penetrating oil and wiggle the flapper as part of your regular future maintenance.
Good luck,
Matt