For years I didn't know that the Palm Sunday Gospel reading is not the triumphal entry Gospel. That Gospel is supposed to be read before the opening procession, from the back (or even outside, wherever the procession begins), as part of an opening ritual. For some, the opening includes the blessing of the palms; for others, at least an opening Palm Sunday Collect and the triumphal entry Gospel.
Then the procession with palms comes. In our parish, all the members proceed with palms, reverence, and return to their seats, during the singing of "All Glory, Laud, and Honor" (the traditional Palm Sunday processional hymn).
This allows for the Passion according the St. Matthew to be read at the place appointed for the Gospel.
Now that Passion is rather long: two entire chapters, 26 and 27. So here is an acceptable way to break it up. I say acceptable, because on the one hand there has long been a tradition of having several appointed readers, and on the other hand, even J. S. Bach's Passions are wont to intersperse hymns.
We pass out a little booklet to every congregant. There are three speaking roles. The subdeacon (or some other suitable, trained man) reads the narrator's part, from the lectern. The celebrant reads all of Christ's parts, from the pulpit. And the parts of all the others in the Gospel (the crowd, Pilate, Peter, Judas, etc.) are read by the congregation.
At several points during the reading, an appropriate hymn stanza is sung. Offhand I recall some of the stanzas from "O Sacred Head," "Jesus, Grant that Balm and Healing," and, one I particularly like, which was employed in Bach's St. John Passion, very near the end, the third stanza of "Lord, Thee I Love with All My Heart." That one is particularly moving, at that juncture.
In similar fashion the Gospel of St. Luke will be read at Wednesday Mass, and the Gospel of St. John on Good Friday.