But "antiquinarianism" is an issue with Pope Pius XII, and John XXIII.
Which way Jesus faced at the Last Supper is irrelevant on that count--as WELL as the fact that the Last Supper was not a Mass.
The Last Supper was indeed a Mass. It was the anticipated sacrifice that would happen on Good Friday.
As to the issue of which way Jesus faced...it wouldn't matter simply for the fact that He is God, and so He could face whatever He wants. This kind of questioning sort of reduces to speaking about Christ in purely human terms, which when carried to its logical conclusion, gives rise to those who seek only the "historical Jesus" - aka Arianism.
"At the Last Supper, on the night he was betrayed, our Savior instituted the Eucharistic Sacrifice of his Body and Blood. He did this in order to perpetuate the sacrifice of the cross throughout the centuries until he should come again, and so to entrust to his beloved spouse, the Church, a memorial of his death and resurrection: a sacrament of love, a sign of unity, a bond of charity, a paschal banquet in which Christ is consumed, the mind is filled with grace, and a pledge of future glory is given to us" (Sacrosanctum Concilium 47).