You wrote:
“It is my understanding that the tradiitional Latin Mass either doesn’t have epiklesis or that epiklesis is diminished. Can you clarify that?”
Yes and no. There is no explicit prayer called the epiclesis, but:
“This is the theory defended by their theologians at the Council of Florence (1439). A deputation of Latins and Greeks was appointed then to discuss the question. The Greeks maintained that both forms are necessary, that Transubstantiation does not take place till the second one (the Epiklesis) is pronounced, and that the Latin “Supplices te rogamus” is a true Epiklesis having the same effect as theirs.” http://www.newadvent.org/cathen/05502a.htm
Apparently this view, that the “Supplices te rogamus” is a true Epiklesis, is still held by Eastern Orthodox liturgists such as Nicholas Cabasilas:
“According to the great Orthodox liturgical scholar and saint, Nicholas Cabasilas, the prayer in the Roman rite “Supplices te rogamus” (”Most humbly we implore Thee”) is an “ascending epiklesis.”” http://www.orthodoxresearchinstitute.org/articles/liturgics/johnson_western_rite.htm
Oops! Nicholas Cabasilas was not a modern liturgist, but a 14th century Orthodox saint.
My bad.
Friends of mine who had suffered many years in Novus Ordo parishes used to tell the following joke:
You know what the difference is between a terrorist and a liturgist?
You can negotiate with the terrorist.
The epiklesis is the supplication of the Holy Spirit to mystically change (i.e. transubstantiate in the western terminology) the bread and wine. My understanding is that the traditional Latin Mass does not call on the HS specifically, but that there are additional prayers that do.
It is also my understanding (from having heard post-vatican II Masses) that the so-called NO Mass does have epiklesis.
Bowing profoundly, with his hands joined and placed upon the altar, he [the priest] says:
Supplices te rogamus, omnipotens Deus: jube haec perferri per manus santi Angeli tui in sublime altare tuum, in conspectu divinae majestatis tuae: ut quotquot [he kisses the altar] ex hac altaris participatione sacrosanctum Filii tui [he joins his hands, and signs the Host and then the chalice with the Sign of the Cross] Cor+pus et San+guinem sumpserimus [he signs himself with the Sign of the Cross] omni benedictione caelesti et gratia repleamur. [He joins his hands.] Per Christum Dominum nostrum. Amen.
We must humbly beseech Thee, Almighty God, to command that these offerings be borne by the hands of Thy holy Angel to Thine altar on high in the sight of Thy Divine Majesty, that many of us as at this altar shall partake of the Body+ and Blood + of Thy Son, + may be filled with every heavenly blessing and grace. Through the same Christ our Lord. Amen.