as per Nostra Aetate and Lumen Gentium your Church [Catholicism] forbids proselytizing jews because it doesn't classify Judaism as a false religion and holds that they have a functioning covenant with God.

Jumping in, I don't read those that way. As a covenantalist, I agree the Jews have a national covenant with God while believers in Christ are the only heirs of the spiritual covenant with God (which Jews can have on the same terms as anyone else by belief in Christ). The Catholics under Cardinal Pizzaballa are still running the St. James Vicariate out of the LPJ, which evangelizes Jews toward Messianism (Christianity within Hebrew culture), and I understand they simply have a semantic quibble that evangelization is not proselytization. However, I also suggest that Protestants have succeeded the most at this particular segment of the Great Commission, having done the most to understand the culture and treat it as pre-Messianic rather than post-Christian.

The covenantal system allows both Catholics and Protestants to be members of the one body of Christ with unique places, beside the Orthodox, and allows Jews to become members as well without losing any Jewish culture (except for those folk Jewish practices that are so easily read as idolatry that Messianics drop them readily).

I don't know who you mean as a gay Jewish drafter of Nostra Aetate, perhaps you're merely metaphorically referring to Jesuit Augustin Bea.