I'll admit it easily. You are right that the Whigs are the best phrases precursors to modern Republicans. But the name and its use in American politics does trace its origin back to Jeffersons party, quick Five second book cite. My point was on the origin of "right" and "left" attribution in American politics, which almost assuredly began with the hamiltonian/Jeffersonian split, largely because the occurrence that happened to produce those terms, the French revolution, happened at the time of their feud. Jefferson, a profound supporter of anti monarchist tendencies in France most assuredly painted Hamilton as a monarchist (which the right in France supported) despite him not being one. I don't have searchable access to the articles written by Jeffersons friends at his urging, but its almost guaranteed Jefferson would have known of the terms, him being secretary of state at the time and having a predilection for France, and would most assuredly have urged the use of its intent if not the actual word in calling Hamilton out, he definitely called him a monarchist frequently. again your point is fair that the assignment is misapplied, largely due to the fact that in reality the founding fathers didn't have much approximating true right wing politics outside of the Tories who were reviled as traitors to the founding country.
To your point about Jefferson being right wing, I can only think of his advocation of gun rights as proof. He wasn't profoundly institutionally religious (big supporter of Jesus' liberal views though with multiple quotes to back that up), he didn't support anti Islam rhetoric, he wrote for social progressivism like in the freeing of slaves (despite having a pretty spotty personal handling of the issue) and, most importantly, he was personally involved in creating the two party system in America for the explicit purpose of fighting off an adversary he saw as too right wing, or too supporting of the monarchy.
He's a complex guy sure, and he is anything if not consistent in places, but attributing right wing tendencies to him is a shade too far. Even calling him a libertarian, which is I think what you mean by"classic liberal", is a little off the mark. There's a lot of him in that term, its true, quite a bit. But I suspect the outcomes of some libertarian policies, notably the laissez faire attitude towards the less fortunate, would rub him the wrong way. There are a lot of quotes by him advocating doing what's right to those less fortunate over doing what is politically consistent or economically sensible (see the argument that caused the rift to begin with). Its also slightly deceptive to use the term classically liberal to hide behind people not inclined to look up what the term refers to and instead attribute it to modern day liberalism. I suspect you're doing that because libertarian has some connotations associated with readers here. Regardless i think its fair to say that in some issues, particularly with his fight over banking with Hamilton, he edges closer to libertarian that right wing anyway.
In any case though, I'm glad for our conversation, it made me look up stuff, it maybe made people reading this look stuff up... And at the end of the day that's what matters. You can hold to being right, its the internet, that doesn't matter, what matters is that people, myself included, looked into some primary and secondary sources to fund their arguments and learned some stuff. That's always a win.
As an aside, I recommend if you're looking for non wiki sources, which I only used for their ease in quick reading, This book that I'm reading now. I especially recommend the audio book format. The reader is pretty good to listen to in the car.