Neither the founders nor the views they espoused fit nicely into the secularist, libertine individualistic box the neo-reactionaries wish to place them into.
You make very good points. I’d just like to comment on the “value-neutral” point. Adams, it should be noted, famously defended in court the British soldiers in the Boston Massacre, indicating that he believed in due process (supposedly something that is “value neutral” according to some “neo-reactionaries”). I think it isn’t so much that neutrality is the end goal of “value-neutral” institutions so much as it is a case of the conflict between outcomes and process. The New Right’s (and the Left’s) mistake is in thinking that if the outcomes aren’t the ones we want, the process must be corrupt and should be replaced. The conservative view (or “tragic” view, or “constrained” view) is that we cannot guarantee outcomes in life and that therefore process (the rule of law) is the thing that really matters. As Ralph said in Lord of the Flies, “the rules are all we’ve got.” Process is what separates civilization from barbarism and therefore “value-neutral” process isn’t value neutral at all.
It's interesting that they all wanted "virtue" as part of the government. The modern American government would appall them all in that sense.
The only thing these men really agreed on was the fact that Britain was doing them wrong and the colonial administration had to go. Once the new country was established, the partisan disputes hidden by the Revolution re-emerged in full force.