It is also not a result of any visions of post-Schism saints, but is rather a discovery of the Sacred Heart within the liturgy.
Can you expand on this?
Perhaps the best place to start is to see what texts from the Divine Office were selected for the Feast of the Sacred Heart. These texts show the Sacred Heart is focused on the sacrificial love of God in Christ. The Introit sets the tone:The thoughts of His Heart are from generation to generation: that he may deliver their souls from death, and feed them in famine.
Ps. 32: 11, 195
The Epistle is Eph. 3: 8-12, 14-19, which ends with:That you and all the saints may understand and know the breadth and length and height and depth of the love of Christ, which surpasses human understanding; and that you may be filled with the fullness of God's being.
The Gradual is taken from Matt. 11: 29:Take my yoke upon you and learn from me, because I am gentle and humble of heart, and you will find rest for your souls.
The Gospel is St. John's account of the piercing of Christ's side.
The Offertory is Ps. 68: 21:My heart is broken with insults and sadness, and I looked for one who would share my grief, and there was no one: for one who would comfort me, and I found no one?
You can also get a sense of the focus from the hymn of first vespers which focuses on our sins which were responsible for Christ's suffering, a recurring theme in the Christian West:Look how the proud cruel multitude of our sins has wounded the sinless Heart of God, undeserving of such treatment. It was this that put direction and vigor into the soldier's hesitation; it was man's sin that sharpened the spear's point. The Church, bride of Christ, is born of His pierced Heart; this is the gate in the side of the ark, put there for man's salvation. Seven streams of never-failing grace flow from this Heart that we may wash our soiled robes in the blood of the Lamb. How shameful it would be to return to sins which would this sacred Heart; how much better to try to reproduce in the burning love of our hearts the flames that are signs of the love of His Heart. Glory be to You, Jesus; from Your Heart You pour out grace; and glory be to the Father and the loving Spirit, for ever and ever. Amen.
All of those interpretations of the symbolism of Christ's Heart can be found in the Fathers. St. Ambrose, if I recall correctly, was pretty explicit in the piercing of the Heart, and the water and blood that issued forth, were the founding of the Church.
This is all a very far cry from the unfortunate visions of St. Margaret Mary that popularized the devotion and took it in a new direction.