Well, it sounds appealing if challenging. But didn't Catholics try that among themselves in V2? As one poster wryly
The last time the church imposed its judgment in an authoritative manner on "areas of legitimate disagreement," the conservative Catholics became the Sedevacantists and the Society of St. Pius X, the moderate Catholics became the conservatives, the liberal Catholics became the moderates, and the folks who were excommunicated, silenced, refused Catholic burial, etc. became the liberals. The event that brought this shift was Vatican II; conservatives then couldn't handle having to actually obey the church on matters they were uncomfortable with, so they left. — Nathan, http://www.ratzingerfanclub.com/blog/2005/05/fr-michael-orsi-on-different-levels-of.html
I think I would benefit from listening to and praying with Xtians who disagreed with me so much that many thought I wasn't fit to be called Xtian.
Which humility is very refreshing. However, as noble as your thought is, my experience (as one who was manifestly born again while still a RC and remained active therein for 6 years after) is that there are very very few that we find fellowship in Christ with. (And one prayer to Mary or some saint is going to nuke that.) For while we often enjoy spontaneous rejoicing on meeting a fellow evangelical type, die to a shared life giving conversion with its profound changes in heart and life, and relationship with the Lord, and Scripture-based walked, with Catholics there is no such fellowship. Instead if they say anything then it is about their One True Church®, and exalting the Eucharist and Mary or indifference or antagonism in inquiring about salvation. But there are exceptions, usually among those of simple faith.
Fellowship with mainline Prots is also seldom realized, as they also know nothing experientially of the transformative New Birth. But regards what Prots can realize re Christ-centered ecumenism, I will let the famous "prince of preachers" speak:
Most atrocious things have been spoken about the character and spiritual condition of John Wesley, the modern prince of Arminians. I can only say concerning him that, while I detest many of the doctrines which he preached, yet for the man himself I have a reverence second to no Wesleyan; and if there were wanted two apostles to be added to the number of the twelve, I do not believe that there could be found two men more fit to be so added than George Whitfield and John Wesley. (C. H. Spurgeon’s Autobiography, Vol. 1, p. 173, in “A Defence Of Calvinism,” The Banner Of Truth Trust edition)
Now I hate High Churchism as my soul hates Satan; but I love George Herbert, although George Herbert is a desperately High Churchman. I hate his high Churchism, but I love George Herbert from my very soul, and I have a warm corner in my heart for every man who is like him. Let me find a man who loves my Lord Jesus Christ as George Herbert did, and I do not ask myself whether I shall love him or not; there is no room for question, for I cannot help myself; unless I can leave off loving Jesus Christ, I cannot cease loving those who love him. (Metropolitan Tabernacle Pulpit, Vol. 12, p. 6; http://www.spurgeongems.org/vols10-12/chs668.pdf)
To be brutally brief, one important difference between VatII and this would be that this would be only about understanding difficult differences. I have nothing like reaching a conclusion in mind.
Also, I do not think the kind of Catholic who would be of any use in this conference would be so stupid as to call on the intercession of the saints in any plenary gayhering5.