If by your lights, Eastern Orthodoxy and Roman Catholicism share the same faith to such an extent that inter-communion should be able to be instituted, what would be the purpose of these missionaries? To what would you be converting them?
The answer, of course, was in your original post, where you stated that the barrier to some sort of union is purely political. Therefore, the decision not to send Roman missionaries east-ward would likewise be political -- i.e. in order to promote union.
The implication is obvious (at least to me) -- sending Roman missionaries into Orthodox lands to "compete for souls" against the Orthodox Church would likewise be fundamentally political. What exactly would these converts be gaining, other than being juridically aligned with the "right" hierarchy? If they would be gaining something more than that, then we obviously do not yet share the same faith, and union would be a farce.
This all points to what the other Orthodox posters on this thread have been saying, and for the most part without rancor (which has no place in this kind of discussion) -- there are profound differences between the basic spiritual approaches of the Orthodox and Roman Catholic Churches.
This, of course, is without even beginning to address the question of just why Roman Catholicism would place a priority on sending missionaries into Orthodox countries when Catholic parishes across the western world are in desperate need of priests to care for their most basic spiritual needs, and when Catholics have hundreds of millions of readily available Protestants (not to mention non-Christians) who presumably need conversion to Roman Catholicism even more badly than do we Orthodox.