I really like to put an OO perspective into this.
I think we all agree that a certain "rival" patriarch was created so that there would be a certain "ecumenicity" and for those who wish to keep traditions while joining the faith they agree with.
Now, keeping proselytism aside, which is something that happens on any side of the coin, I think one should also look at the history of the OO's and factor this in. For the OO's, especially Syria and Egypt, we had rival EO denominations, and we still do, although we live much more peacefully today (in fact, we're practically sister churches). The point is we should never ever fool ourselves in thinking that these rivals were created for unity's sake. They were always created as rivals. This is the truth that we have to face. EO's and OO's in Egypt and Syria faced it, and they now love each other.
It's a fact that people have to accept and it can't go away. If one day the Eastern Catholic churches reach a faith agreement, where it is possible for one communion to occur, then we should just accept one another for now. I'm not saying that there should be two or three patriarchs in one city, but I'm saying that this is an inevitability that needs to be dealt with for now, and then when unity occurs can be fixed later.
Perhaps, I can also give a local example. In our Coptic Archdiocese here in NJ/NY area, we have two cities where congregations created rival churches, two in Staten Island and two in Bayonne. What was the solution for the split? Let's create two, and if it works out, then in the end we would have two peaceful churches. While the history may be bad, and I'm not saying ignore the history, the future should be towards reconciliation and a way in which history should never repeat itself. As the EO and OO churches of Alexandria and Antioch look at each other, we see each other not anymore as heretics, but as successful churches, defending Orthodoxy side-by-side.
Therefore, I think the existence of the Eastern Catholic churches should never be an impediment to dialogue. They're there now, and we should just have to accept their existence until we can reach a solution.