S1E I dont think it will be up to EDI or GLA to "allow the strategic decision to go forward". The passengers and airlines will decide and there will be very little that the airport owners can do about it. That, although admittedly only on a European scale so far, is what has boosted Edinburgh to its predominant position in Scotland. Inbound tourists want to fly there from the major population centres in Europe, and our businesmen want to fly out to these self same cities. Best of both worlds for the airlines.
Edinburgh not a 21st Century airport? Arguable, but since its most recent developments I'd put it way ahead of all of the comparably sized and smaller English regionals (BHX, LTN, EXT, BRS, EMA, NCL, etc) that I've flown through in the last few years. As for LHR and LGW, probably the worst major national hubs in Europe, both completely snookered for further development, and no relief coming from new build elsewhere in the SE to offer relief if the government keeps to its present policy. That fact too will be of help to Edinburgh as airlines are forced to go elsewhere.