Here's Byrd's setting of the introit for Pentecost, sung by the DC-area group Countertop Ensemble. It is preceded by the same text, presented solo on an office responsory tone.
Sure, for most churches, a five-and-a-half-minute introit is too long for the action, but in the right circumstances - a delayed entrance, a decorously slow procession,a largish church, an incensation of the altar - the timing could fit. It would require that all the involved liturgical ministers contribute: servers, server trainers, and the clergy, along with the schola. Has your parish looked for ways to put beauty first in the entrance procession? Man does not live by efficiency alone!