First off, welcome to the Forums!
As for things like the three-bar cross, I don’t recall ever seeing anything to indicate that it’s been forbidden, at least not by Rome. It sounds like the Ruthenian Church has a very strong “Latinized” contingent, even/especially among the Bishops, and that may be why such traditions disappeared.
Rome is not Eastern Christian territory. Go to the Ruthenian homeland in places like southeastern Poland and northeastern Slovakia (which are Latin Rite countries) and you will see that the three-bar cross is disappearing in Byzantine Catholic churches. In Transcarpathia, which is part of Ukraine, which is predominantly an Eastern Christian country, the three-bar cross still exists.
While many Byzantine Catholic Churches in the U.S. may still display the three-bar cross, in Eastern Europe, which is the homeland of the Ruthenians, this is not necessarily true in those countries that are predominantly Roman Catholic (Latin Rite).
During Soviet rule, in countries like Poland and Slovakia, the Byzantine (Greek) Catholic Church was outlawed. They were either turned over to the Orthodox Church, closed, or destroyed. It was only after the fall of communism that the Byzantine (Greek) Catholic churches were returned to Rome.
Unfortunately, during nearly fifty years of Soviet rule, the Byzantine Catholics had no church to go to except the Orthodox church. So many remained Orthodox. So today, many former Byzantine Catholic churches are being used for Latin masses–or hold both Latin masses and Byzantine liturgies.
The priest at one such church told us that the instruction to change the three-bar crosses to two-bar crosses originated in the 1880’s. But there was some leniency. The change only had to be made when the church made repairs or other changes. So it took many years before you started seeing the results. When communism fell and the churches were returned to Rome, many were in disrepair after having been closed for so many years. So when the churches were repaired, the three-bar crosses were turned into two-bar crosses.
I, frankly, don’t know if or how this applies to Byzantine Catholic churches in the U.S.
I do know, however, that very little of the liturgy is sung in the Old Slavonic anymore. The Ruthenian ethnicity seems to no longer be part of the church, which is now serving a much more diverse group of parishoners. But I sure do miss the old times!!