I'm curious why you'd say that you wouldn't "buy" Britain being the strongest power in the 1770s.

Keep in mind that the 18th century was not a period where there were runaway superpowers as in the 20th century, yet Britain fairly clearly was on the top at the time. In the 1760s Britain had just fought and won the Seven Years War (effectively the first true world war) as a coalition with Prussia et al against France and Spain et al. Britain won many concessions from that and an enormous amount of territory (including Canada), they were definitely riding high militarily in the 1770s. Not long after, Britain would eventually win the Napoleonic wars and, arguably, the war of 1812.

A few things are notable in regard to the dominance of British power in the late 18th century.

First, the Royal Navy had been the largest in the world from the 17th century onward. Second, the British ended up on the better end of most major conflicts they were involved with at the time in the end with the notable exception of the American Revolution. Most importantly, the British tended not to be defending what they already held and were often fighting to expand or control territory or to gain dominance over another power. Most often, when the British lost a war at that time it wasn't that they lost something they already had but rather that their ambitions were thwarted (with that notable exception, of course).

Compare that to some of the other competing great powers at the time such as France, Spain, and Prussia. In 1808 Spain was effectively taken over by France, and the Spanish empire was dwindling from 1790 onward. Prussia similarly faced major defeats on its homeland during the Napoleonic wars, barely hanging on to power long enough to return after Napoleon was gone. And we know what happened to Napoleon's rule and the French Empire. Every other major power at the time had to come to grips with major loses of territory to other major powers and lapses of sovereignty. Britain never faced a serious risk of losing sovereignty during that time and for the most part expanded its territorial control. Even with the huge loss of the American colonies the British Empire continued to grow at an incredible pace throughout that period. And certainly prior to that loss it would be difficult to seriously peg any world power as superior to Britain at the time.