“I’m curious, what is the source contradicting Moravians’ own claim of having origins in the Orthodox?”
First, produce an actual claim from the Moravians that they were never Catholic but were instead Eastern Orthodox. Until you do that I have no reason to believe you can validly claim that they claim that.
“The Catholic Encyclopedia doesn’t contradict them as you have:”
I think you need to read the sources you quote more closely:
“HISTORY OF THE ANCIENT UNITAS FRATRUM (1457-1722)...”
Thus, we see already that the old Catholic Encyclopedia is clearly referencing a group that could only be Catholic if it started in Bohemia in 1457.
“The Bohemian Brethren are a link in a chain of sects beginning with Wyclif (1324-84) and coming down to the present day.”
Wyclif - a Catholic who embraced heresy. Not Eastern Orthodoxy.
“The ideas of the Englishman found favour with Hus, and Bohemia proved a better soil for their growth than England.”
Hus - a Catholic who embraced heresy. Not Eastern Orthodoxy.
Produce a source from the Moravians themselves, preferably from an official Moravian source.
The movement that was to become the Moravian Church was started by Jan Hus (English: John Huss) in the late 14th century. Hus objected to some of the practices of the Roman Catholic Church and wanted to return the church in Bohemia and Moravia to what were the practices in these territories when it had been Eastern Orthodox: liturgy in the language of the people (i.e. Czech), having lay people receive communion in both kinds (bread and wine - that is, in Latin, communio sub utraque specie), married priests, and eliminating indulgences and the idea of Purgatory. Evidence of their roots in Eastern Orthodoxy can be seen today in their form of the Nicene Creed, which like Orthodox Churches, does not include the filioque clause. In rejecting indulgences, Jan Hus can be said to have adopted a doctrine of justification by grace through faith alone; in doing so, the Moravians arguably became the first Protestant church.