I understand the doctrine that the Roman Catholic religion is the one Church founded by Jesus Christ and as such it provides all the means of grace whereby man can best acheive union with God. I am wondering, because of this, is there conclusive proof readily available showing that Roman Catholics are the most moral of people?
The evidence is the saints of the Catholic Church, if you look at their lives you will see what the most moral life is.

Because they are the people who lived most like Christ.
‘Humble yourself before God; lose yourself in the very depths of that sacred desert of which I have, spoken to you; be absorbed by the Sovereign Good, consumed by the sacred fire of love.’
St. Paul of the Cross
‘Oh! Lord, I desire thee wholly, for in thy clear and strong light I see that the soul can never be at peace until she has attained her last perfection. Oh, sweet Lord! if I believed that I should lose one spark of thee, I could no longer live.’
St. Catherine of Genoa
‘Blessed the one who seated in his cell like Angels in heaven keeps his thoughts pure and with his mouth sings praise to the One who has authority over everything that breathe.’
St. Ephrem of Syria
‘Wherefore, it is supreme ignorance for the soul to think that it will be able to pass to this high estate of union with God if first it void not the desire of all things, natural and supernatural, which may hinder it. . . for there is the greatest possible distance between these things and that which comes to pass in this estate, which is naught else than transformation in God. For this reason Our Lord, when showing us this path, said through Saint Luke: Qui non renuntiat omnibus quoe possidet, non potest meus esse discipulus. This signifies: He that renounces not all things that he possesses with his will cannot be My disciple. And this is evident; for the doctrine that the Son of God came to teach was contempt for all things, whereby a man might receive as a reward the Spirit of God in himself. For, as long as the soul rejects not all things, it has no capacity to receive the Spirit of God in pure transformation.’
‘. . .Perfect love of God renders death agreeable, making the soul taste the greatest sweetness therein. The soul that loves is inundated with a torrent of delights at the approach of that moment when she is about to enjoy the full possession of her Beloved. On the point of being delivered from this prison of the body, she seems already to contemplate the glories of Paradise and all within her is transformed into love.’
St. John of the Cross