Interesting question you pose, the one part that jumped out to me is the referencing to converting people to Catholicism - if by this you mean from Protestantism. This makes me uneasy as their is more than enough evangelization opportunities around with just the Non Christians out there. Not sure why evangelize one group of Christians to join another. This goes both ways, also uncomfortable with Protestants going around trying ‘convert’ Catholics. If after study and prayer you come to the conclusion to join the Catholic Church, well thats great go for it. But to actively go around and try convert one branch of Christianity to one of the other two seems waisted energy.
Ecumenicalism for me is to understand each other in a charitable way, minus all rhetoric, hyperbole, and half truthes. At least the NonChristians can observe us acting like mature adults rather bickering all the time and counting score of our argumentive “win’s”
Sorry this is a bit of a ramble but those are my two cents
