The UGCC did have property stolen from the Communists, because that propert was Polish an Romanian until 1945. The Communist also stole property from the Greek Catholic eparchy of Munkachevo, in Czechoslovakia until 1945.
It also stole property from the Orthodox jurisdictions in the area of the 3 countries mentioned, when the respective areas were annexed to the USSR. Such was the case of Pochayiv, which belonged to the Orthodox Church of Poland. So, the MP has no business in the issue. It is true that before WWI, Pochayiv belonged to the Russian Orthodox Church (but not the MP, because the patriarchate was abolished). But even earlier, it was Greek Catholic for some time, and before that, it was Orthodox under Constantinople.
So I would strongly suggest maintaining state ownership...
...because possession is nine tenths of the law (that's an Americanism).
As I mentioned before, the canonical basis of the Orthodox Church of Poland's autocephaly was questionable, something not cured until 1948. In the meantime between 1945 and 1948, Pochayiv was very much the MP's business: that the EP stuck his nose in that business doesn't change that.
It has been Orthodox under the Patriarchate of Moscow's Metropolitanate of Kiev and All Ukraine for the last two decades, although the UOC-MP does not own/posses it.
It refused to go into schism with the UOC-KP. Hence it has never been Orthodox under the UOC-KP.
For the 44 years before that, it was undisputedly Orthodox under the Patriarchate of Moscow's Exarchate of Kiev and All Ukraine.
For the 25 years before that, it is disputed that it was Orthodox under the same Patriarchate of Moscow's Exarchate of Kiev and All Ukraine.
The UAOC tried to seize it with Bolshevik, then Nazi, help, but the Lavra resisted. Hence it never was Orthodox under the UAOC.
It was Orthodox for disputedly 25 years under the Orthodox Church of Poland.
Before that, it was Orthodox under the Russian Holy Governing Synod (in loco patriarchi) for undisputedly 91 years (and the 25 disputed years thereafter).
The Vatican occupied it before that for 110 years. It has stood for at least 485 years, perhaps 700. So the Vatican had it in its gripped for but a short time. Prior to that, it had been the publishing center of the opposition to the scheme of Brest:the press was taken, during the persecusions of the Polish Republic, to Jordanville for the Russian Orthodox Church Abroad, and now, as before, publishes for the Patriarchate of Moscow.
Before that, it was Orthodox under the Patriarchate of Moscow, for 34 years.
Before that, it was Orthodox under Constantinople's suffragan the Metropolitan of Kiev, Galicia and All Rus'/Little Rus' for 54 years.
Before that, it was Orthodox illegally (the UGCC alone have legal possession of all Orthodox properties in the PL Commonwealth) under Metropolitans of Kiev, Galicia and All Rus'/Little Rus' consecrated by the Patriarch of Jerusalem for Constantinople, who sought reunion with Moscow, for 12 years.
Before that, it was Orthodox illegally but under no on after the Metropolitan of Kiev's apostasy and submission to the Vatican and the bishops of Volhynia and Lutsk (the local bishops for Pochajiv) personally going to the Vatican to grovel and kiss their supreme pontiff's slipper, for 25 years.
Before that, it was Orthodox briefly under the Metropolitan of Kiev, Galicia and All Rus' consecrated in Vilnius by the EP after the elevation of the Metropolitinate of All Rus' into the Patriarchate of Moscow and the translation back of Kiev from Moscow to Constantinople, for six years, the Metropolitan of Kiev so consecrated promptly apostacizing and submitting to the Vatican.
Before that, it was Orthodox under the Metropolitan of Moscow and All Rus', all 64 years of its recorded history to that point. For the 77 years of its prehistory it was Orthodox under the same autocephalous Metropolitan (even the Vatican's minions the King of Poland/Grand Duke of Lithuania managed to recognize and accept that), and the 149 years before that Orthodox under his autonomous predecessors in Vladimir/Moscow suffragans to Constantinople, and the legendary half century or so before that under his autonomous predecessors the Metropolitan of Kiev and All Rus' sponsored by Galicia but based in Vladimir and other Russian (in the modern sense of the word) and cities/sees and under Constantinople.
Sooooo, that means it has never been Orthodox under the UAOC nor UOC-KP, the Orthodox Church of Poland claimed it for 25 years, it was in the grip of the UGCC for 110 and claimed by it for an additional 37 years, it was Orthodox under Constantinople 60 years in addition to 12 years illegally but canonically under Constantinople, and it has been Orthodox under Moscow for 263 years-including the last 181 with only 25 years disputed (but no longer)-of its recorded history and 149-199 of its legendary history Orthodox under Vladimir/Moscow when its primate was autonomous under Constantinople-moot, as Moscow isn't going to lose its autocephaly.
Not a hard call.
Of course, what it should be, and soon, is Orthodox under Kiev, an UOC-MP become autocephalous.