Some of the people on thsi thread seem to have very odd ideas about the power of the Monarchy in the UK political system....

Well quite- if the King pushes things too far he'll just end up being forced to abdicate anyhow.
I think to get what the original poster wanted, which presumably is a relatively pro-German Britain, you need to start earlier and not concentrate on Edward VIII. The 1931 political crisis panning out differently would be a start, ideally with Mosley or Lloyd George heading up a slightly different National Government. Emphasise establishment pro-Germanism (or anti-Communism) and that might give you a British foreign policy that's friendlier to British interests. It still won't be pro-Hitler as such, but more willing to turn a blind eye as long as the Germans keep their focus firmly on the East and don't overstep the mark.
It's worth making the rather hackneyed point at this stage that even a full-bloodedly Fascist Britain is not neccesarily pro-German by any means. If the Nazis try anything funny- pow, JFC Fuller's Expeditionary Force goes to the continent, and it's probably a lot more potent than OTL.
Of course the problem with all of this is that it isn't much to do with our David- if he avoids Wallace Simpson than he won't have to abdicate, but he isn't any more powerful or influential than George VI was either. To be honest though, I don't think he ever really can be, barring a very dramatic PoD or something so early that there's no Hitler to deal with anyhow.