John Birch Society
The John Birch society was founded in 1958. The influence of JBS on American conservative Catholicism in the 1960s was enormous. Much of their thinking regarding anti-communism, freemasonry, and New World Order comes from the JBS. This is exactly the kind of material Schuckardt was using on his talks in the 1960s. He was able to connect with other Birchers throughout the country.
In case you think this is overstated, here's former JBS president John F. McManus talking about modernism, Pius X, and with Fatima in the background:
Many of the people who eventually joined Schuckardt first connected with his ideas through local chapters of the John Birch Society. These were conservative Catholics who were also heavily involved in far right politics. Today they downplay this, but without the JBS, it's unlikely that Schuckardt would ever have found such radicalized people willing to embrace his highly political anti-communist version of conservative Catholicism.
Anarchy U.S.A. (1965)
This movie was heavily promoted by Schuckardt and was shown to children at the Espiritu Seminar (annual summer camp). It can't be overstated how important anti-communism and the John Birch Society was to the thinking of Schuckardt and the TLRC. Much of the group believed in this stuff.
Archive.org page on Anarchy U.S.A. (1965)Other Sources
If you google "John Birch Society Catholic Church" you see a lot of Catholics were into this stuff in the 1960s, long before Vatican II. Of course, the traditional Catholics may just dismiss them as modernists.
Newspaper ArticleHere's a new book on Robert Welch. My guess is the TLRC members were just repeating what they were getting from the JBS.
Robert Welch BookThe JBS is always heavily involved in the "America First" movement which is still popular with traditional Catholics.
JBS Video: America FirstMonarchism has been popular with conservatives for a while
Rise of Monarchism