What if During the ARW, the British suffer a even stronger defeat then they did OTL. I.e. they lose all of their colonies in the America's and lose their foothold in India. You can't really call the British an Empire if they don't have ether of those.
I think the British Empire suffering the loss of its entire Empire in one go is probably pushing it - by and large European diplomats knew when enough was enough in this period and didn't like to utterly destroy their enemies, probably mostly for fear that the same would happen to them in retribution. On top of this, I don't think that in 1776 and beyond the French are in any position to take Britain's Indian holdings away.
I'd have to agree that the only real way this is likely to happen is if England turns into a stagnant European second-rate power, for instance the idea proposed where James II keeps the throne. I'm not convinced by the Spanish Armada idea for two reasons on opposite ends of the practicality scale: to be ultra-realistic, the Spanish Armada isn't far from being a 16th century Sea Mammal. It was simply never going to work. Case in point, Parma (who was due to march 24,000 men to Flanders to be the invasion army) simply refused to follow orders as he was so convinced it could never succeed, and marched off to fight the Dutch instead. On the other end, if we assume a POD where somehow the Armada succeeds, the result would not be an England under Spanish occupation in the long term (in the short term maybe but not long enough to ruin colonial plans) and the history of the Americas suggests that Hapsburg England would have to be in a diabolical mess to miss its window for colonising the Americas, since 100 years later the Dutch, Swedish and English were still trading control of relatively small parts of what would become New Jersey. 100 years plus is an awful long time for Spain to unintentionally keep England under a military occupation which prevents it from colonising - especially as the more likely alternative is that a Hapsburg King of England would after a generation or two after the Armada start to become very jealous of his Spanish brethren's Empire...Also you could argue that a Hapsburg England might imperil the very existence of the Dutch state, and at least could do an efficient job of cutting off its route to the Americas, meaning that you could potentially lose the most enterprising alternative coloniser of North America. You are essentially the left with France, who was never what you'd call lively at planting colonists.