If a person decides to live his or her life contrary to God and His law, how can that person be said to be "seeking the Lord in good faith?" How can this statement be reconciled?
It seems to me the Pope's comment is congruent to yours. "...Seeking the Lord in Good Faith" suggests they are changing to be in the good grace of the Lord. That is, they are repentant and reformed. Note, "being gay" is no more a sin than being afflicted with Down Syndrome. It's the knowledge and behavior the begets sin.
We are not suppose to judge the souls. That is for God. But we can judge behavior and speculate on what God thinks of that behavior. That said, true Reconciliation starts in the heart, of which only God knows the purity of intent. A murderer that confesses his sins but does not "firmly intend, with God's help, to sin no more and avoid anything that leads to sin" is NOT necessarily forgiven. But that is God's place through the Holy Spirit, not even the Pope's.