Moreover, "limited government" in the context of American founding principles refers to the allocation of responsibilities between states and the federal government, not the overall scope of government.

There is, in fact, a principled originalist argument for universal healthcare. First, it has always been assumed that the states have the power to provide for the welfare of their citizens, as well as to police their behavior and morals. The states are, in that regard, decidedly not "limited governments" of "enumerated powers." State-level universal healthcare is contrary to no founding principle.

Second, the Commerce Clause was incorporated into the Constitution to allow the federal government to solve what we today would recognize as economic collective action or free-rider problems. At the time it was aimed to address the collective action problem of free trade. It's good for the United States as a whole, but individual states have a short-term incentive to erect trade barriers. The purpose of the Commerce Clause was to allow the federal government to counter-act those short term incentives. Precisely the same problem exists with state-level universal healthcare. Even if most people in a state want it, they can't enact it because it's too easy for people from neighboring states to free-ride on those services. The Commerce Clause is thus properly invoked for resolving that problem at the federal level.