What democracies, of whatever sort, did US founders know about?

Oh what a circus, oh what a show!

Point is that England was a monarchy then and still is, expanded to the UK.

Not really. Oh they do have a Monarch, but they are a parliamentary democracy.

And during the Cromwell years, there was no monarchy.

No, a later Act of Congress, well after the Civil War: Posse Comitatus Act - Wikipedia

The Icelandic Democracy?

The current Queen Elizabeth is not descended from anybody who ruled England between 1509 and 1603. That’s hardly a continuous monarchy.

While I don’t disagree with you, even taking out the 11 years of the Commonwealth and a few more for luck, that’s still 400 years since 1603. So not a bad run.

OB

I’d say it’s more than a few more - correct me if I’m missing something, but I believe she also isn’t descended from anyone who ruled between 1625 and 1714.

I presume Adams was talking about “pure” or “direct” democracy, as opposed to republicanism. In the Federalist Papers, the authors extensively cite the failure and breakup of the various leagues and alliances of classical Greece. They claim this as proof that a union of sovereigns such as under the Articles of Confederation is inherently doomed, and that a federal structure where the members cede some of their sovereignty to a national government (one that is NOT merely the embodiment of their alliance) is necessary.