Conservatives had many qualms, but there was no Thermidor, still less an aristocratic and legitimist reaction like that of Europe in 1815. There had never been a base for real aristocracy. The colonial bourgeois elite was not destroyed, only divided and weakened. Moreover, American conservatives were not romantic reactionaries, but Whigs and moderates.The last sentence of this passage would seem to contradict Corey Robin's argument in The Reactionary Mind (2011, pb. ed. 2013) that conservative and reactionary are basically interchangeable categories. But perhaps the difference here is less substantive than terminological. According to Corey R., the "priority of conservative political argument has been the maintenance of private regimes of power -- even at the cost of the strength and integrity of the state" (p.15; italics added). It is subordination and hierarchy "in the family, the factory, and the field" (p.15) -- more than in the polity -- that conservatives have been concerned above all to defend. So if the "conservatives" in America in the 1780s were primarily concerned with 'order' in the public realm, then perhaps, in the framework of The Reactionary Mind, they were not conservatives at all, but merely traditionalists (see ibid., pp.22-23).
Another point might be that if conservatism in its recognizably modern form(s) arose in response to the French Revolution (ibid., p.43), then, perhaps, no responses to the American Revolution should be classified as conservative. (And didn't Burke himself favor independence for the American colonies?)
P.s. (added later): May, p.99, discussing the Constitutional Convention: "Most of the opposition to the adoption of the completed plan [i.e. the Constitution] reflected no fundamental difference of ideology.... It seems to me doubtful whether the Constitution could have been either framed or adopted if the Convention [of 1787] had been held only a few years later, when the Moderate Enlightenment had been challenged by a new kind of revolutionary ideology and most moderates had become reactionaries."