There is a Ukrainian Orthodox chant melody that matches the melody of a Soviet revolutionary song. I think that the latter is Smelo tovarischi v nogu. (Bravely, comrades, on foot.)
Which chant melody? I'm listetning to the song you wrote and I can't associate it with any Ukrainian chant.
I am inclined to think that it is one to the Theotokos. I am not 100% certain it's the particular Soviet song I pointed to I heard the correlation to a Soviet revolutionary song at one or two Ukrainian Orthodox Churches in the USA about a year ago.
I think that the melody includes the point where it repeats:
"братский союз и свобода Вот наш девиз боевой".
The reference in the Soviet song I pointed at to the "Kingdom of Liberty" may hint at it's origin in the Ukrainian chant. When I heard the song the first time, then after the service when we were in line to venerate the cross I talked to a person maybe 50 years old and pointed out the melody's resemblance to it for him. He listened carefully as I sung the Soviet lyrics and he agreed.
My guess is that it's an adaptation from the Ukrainian hymn, rather than the other way around. The Ukrainian Orthodox Church generally came to the US in the 1900-1950 period, and I think that in coming over in that time era, the Church preserved the song melody. It is less likely that they still sing this melody in Orthodox churches in Ukraine, where some melodies could have changed in the last 60 years, but I am not sure.
I do know that the immigrant US churches from Ukraine even in the OCA preserved at least a few West Ukrainian "folk" liturgical styles and melodies that are not in the "High Russian" style.