Czech and Moravian music are rather different - broadly speaking Czech music is part of a continuum with regions to the west while Moravian music is the westernmost extension of the idioms of the Danube basin. Oompah bands are Czech (and German, and Austrian), fiddle/clarinet/dulcimer is Moravian (and Hungarian, and Romanian).

I find it rather hard to believe there would have been enough trombones in Moravia to make the trombone band possible. Maybe the American Moravians happened to live near Elkhart, Indiana and got them at trade price from the Conn factory?