What are your thoughts? Would you work for a church not your own? Do you think it's possible for these sorts of arrangements to work on a sort of "mere Christianity" common-ground? Obviously we don't preach different gospels, but I wonder if the devil is in the details when it comes to this matter.
Yes. Specifically I would work for any Nicene-compliant liturgical church upholding traditional values on human sexuality and opposed to abortion (or if in a mainline church I would work to replace its leadership), although at present I’m not well enough to work for my own church.
More specifically, I would be happiest working for Eastern Orthodox or Oriental Orthodox and to a lesser extent the Assyrian Church of the East or a Continuing Anglican or Old Catholic Church. i would have enjoyed working for the Roman Catholics before the full agenda of Pope Francis became evident, which also bolstered my preference for the Patristic polity where all bishops were equal and the patriarchs of the autocephalous churches served as the primus inter pares of their Holy Synods. Within Eastern Orthodoxy there is a formal honorific hierarchy, which is approximately something like Constantionople, Alexandria, Antioch, Jerusalem, Moscow, Georgia, Serbia, Romania, Bulgaria, Cyprus, Greece, Poland, the Czech Lands and Slovakia, Albania, North Macedonia, and the Orthodox Church in America (I include my church last because the Greeks refuse to recognize its status as autocephaly, claiming that only the Ecumenical Patriarchate can issue a Tomos of Autocephaly, which is simply not the case). The Oriental Orthodox I believe improve on this because while each individual OO church has a hierarchy, there is no hierarchy above that level. Thus within the Syriac Orthodox Patriarchate of Antioch the Patriarch outranks the Maphrian (a sort of vice-Patriarch in charge of the church of India but historically in charge of the church outside of the Roman Empire, chiefly in what is now Iraq, with the Patriarch being in charge in the Roman provinces of Syria and Syria Palestina). The Armenians likewise have a hierarchy of four autocephalous Armenian churches that are part of the larger Oriental Orthodox communion: the Catholicos of Holy Etchmiadzin and All Armenia, followed by the Catholicos of the Great House of Cilicia (which originated from the period when the Byzantine Empire was protected from the Saracens by two Armenian kingdoms, Armenia proper and the Kingdom of Cilicia, which guarded the eastern parts of Asia Minor like twin fangs, but alas it was not enough to stop the Ottoman hordes), followed by the Armenian Patriarchate of Jerusalem and the Armenian Patriarchate of Constantinople. However the Armenian Apostolic Church, the Coptic Orthodox Church, the Ethiopian Tewahedo Orthodox Church, the Eritrean Tewahedo Orthodox Church (both formerly a single autonomous church under the omophorion of the Coptic Orthodox Church) and the Syriac Orthodox Church and somewhat related Malankara Orthodox Church are all equal, which I quite like.
In your case, you could work for a church the Roman Catholic Church has solid ecumenical relations with - a good way to identify those is to see which church often has local bishops or cardinals visiting. For example, the Orthodox, some Anglicans, some Old Catholics, and the Assyrian Church of the East.