However, the question still remains. Why would America's counterparts of Ultramontanism (Sobran, for example) adopt the very un-Catholic, un-Ultramontanist doctrine of rights libertarianism as their message? Why not simply shout "Throne and Altar?" I believe at least the elder (late) Brent Bozell openly identified with the Spanish Carlists and refrained from posing as Thomas Jefferson.
For whatever reason the First and Third strands of conservatism you mention seem to have blended into a single stream. But it still doesn't make any sense.