The Slovaks are a separate GCC, period…
I am not sure that what you have written is completely correct. The Slovak GCC, as a particular church (in the VII sense as opposed to the diocesan sense), has not been in existence very long. Certainly its existence does not antedate the earliest developments of the BCC in America. Until the twentieth century there, of course, was no Slovakia and no Slovak Church. Nearly all if not all, of the GCs throughout Austria Hungary were connected to the mother church of Uzhhorod/Mukachevo. Presov, in NE Slovakia, became a separate eparchy in 1818. This event was similar to the creation of the Passiac, Parma, or Phoenix eparchies in the US. Even in the aftermath of WWI Czechoslovakia included the Zakarpatskaja oblast which was only incorporated into Ukraine after WWII.
So in the early immigration to the US the “nash”, people from the Hungarian lands of Austri-Hungary - whether from Prjashev, Mukachevo, etc., and whether they spoke, Rusyn, “Slavish”, Hungarian, etc. - all of these people would naturally have formed parishes with each other or connected to each other under the same bishop. They would seen each other as members of the same church, and are now part of the sui juris BCC. I don’t see how there could be any canonical connection to Slovak, Hungarian, etc. particular churches. All of thw subdivision into particular churches that follow national lines (even the intriguing connection of the Czech exarchate to Uzhhorod) happened long after these people came to the is and forged the BCC.
The canonical situation for more recent immigrants may be different for more recent immigrants, I suppose. But the idea that “Slovaks” are somehow under the care of the BCC in America, but are canonically part of another church, doesn’t seem correct.
Am I misinterpreting you?