IMO, compromising one's theology, and presummably salvation, to combat a common foe wouldn't do well to fill the pews. It is very likely that the die hards that are still attending services on both sides are the most strident of believers in their particular faiths. Seriously, you either believe the way you believe or you don't.
No theological compromise is needed. As an Eastern-rite Catholic, I am living proof that one can be Eastern Orthodox, but be in union with Rome.
It's not the same as between Protestants and Catholics. BXVI's theology is heavily infuenced by Russian Orthodoxy to begin with.
There are already a small number of Russian Byzantine Catholics.
http://www.byzantinecatholic.org/Heritage/RussCath.html