Fly,
Originally, you asked who we say are the other sheep. At this juncture, it sounds like you seek proof that the other sheep are in fact the Gentiles. Contextually and historically it makes sense, but beyond that, about ‘proof’, why do you say Jesus performed miracles? We believe that part of it was His desire to reveal His divine power.
Recall that Thomas wanted proof, and we know how Jesus responded. Yes- faith is evidence of things not seen, but the historicity, the ‘proofs’, of the Church will blow your mind.
Also, I know YOU believe in Exodus,
but can you get me to believe, if I’m a pagan? (You call sharing your faith Gathering Israel, we call it Embracing Our Cross. Just kidding! …that was a little joke)
The challenge for your obviously serious attempts to have your question answered is that on a thread like this, you have opinions and opining from laity like myself.

and bad jokes. You have a VERY good question, one that I would recommend you settle with yourself; use the Catechism, the writings of the Fathers of the Church, look through some of the very good blogs and websites from people like Madrid and Akin as well. I understand that you as a member of the LDS church would not hold them to necessarily be authoritative, but you may better understand why Catholics believe in contrast to what Mormons believe. And set us straight, you might be thinking!
I have read the BOM and have (had, I lost it in moving) a book by Hugh Nibley, some others by Paul Dunn (sp?) and a copy of the JS Translation of the Bible.
Reading some of these taught me about LDS history and doctrines; I don’t know for sure if what I suggest will help you? But I do know for sure that the Enemy loves it when we hate each other, so I leave you in Christ’s peace and love.
God Bless You!