I don't think Proselytism is as significant of an issue perhaps when dealing with the Eastern Catholics. Rome would have to clarify their existence and force them to become Latin Rite like the rest of Roman Catholicism or allow them to schism. Rome would have to abolish the Eastern Catholic eparchies in the United States and elsewhere and force them under the nearest Latin Rite Diocese/Archdiocese.
Most Eastern Catholics (further: ECs) certainly start out that way as a result of their parents' choice to baptize them in that communion. However, as adults, they remain ECs by their own choice. Their disappearance and/or absorption have wished for by the more polemical on both sides of the East-West Christian divide, but such a wish is unrealistic.
"Force [Eastern Catholics] to become Latin Rite" how? And would this not violate the 34th Apostolic Canon? Would this not be exactly the sort of overbearing, egregious exercise of papal primacy that is at the heart of the problem? Might this not become a repetition of what happened in the Antiochian and Alexandrian churches in the first millenium? And who would carry out the dictum? There is no Empire to enforce this sort of thing? And would not the press have a field day? "United Catholic-Orthodox hierarchy expels 100+ bishops." And what of the Eastern Catholics' own wishes? Are their wishes not to be respected, and have they no right of self-determination?
"Allow them to schism" ... I'm not sure what the implication is. Do you mean to schism into their own, non-canonical (from the view of a newly reunited Rome-Constantinople) jurisdiction? But this would seem to oppose exactly one of the major complaints of the Orthodox vis-à-vis Uniatism, that union merely resulted in a different schism. "God persuades, He does not compel; for violence is foreign to the divine nature" [Letter to Diognetus, 2nd c.]
"Rome would have to abolish the Eastern Catholic eparchies" ... Presumably, you mean that the eparchies of the current Orthodox communion would be preserved. Very well, but which ones? Who would be protos in the United States, for example? The Russian metropolitan? Or the Greek? Or would the country be split into Alaska and northern west coast for the former, and the rest of the country for the latter? And who decides? Or ... since the diocese of the (RC) Archbishop of Baltimore would be the oldest founded among all the dioceses of the putatively reunited church, would all of the present Orthodox parishes come under the jurisdiction of the local Latin bishop?
I think that there is far too little realization, by both sides, of the desire, yes, historically, but even to the present day, of the current EC churches to be/remain in communion with both Rome and Constantinople. This was certainly the case with at least the Melkites, who managed to maintain communion far beyond 1054 (let alone 863), possibly as late 1724, and the Ukrainian bishops, who managed the same through at least the Tatar onslaught (1240). Regardless, the affinity for Rome that resulted in the unia is ofter far overinterpreted as a desire to become Latin. Where Rome and Constantinople to be reconciled, rest assured that the EC churches would unite with their counterparts in the Orthodox church, not with the Latins, and schism. With respect to the largest of the Eastern Catholic churches, the Ukrainian, one thing that surely will not happen is a forced union with the Moscow Patriarchate - the recognition of the claims of Moscow by Jeremiah II was one of the issues that helped decide the question of union little more than a decade later.