Our priest does not chant it. He reads it sotto voce, such that we can hear from the back that he is reading it, but not make out the words. No singing. I don't recall any Colloquium EF Masses where the priest sang any propers.

gregp--when you say 'no singing', are you referring to the priest? I have edited my original query to try and make it more exact but may have just muddled it up.

No, at a Missa Cantata the priest does not sing the communion antiphon or recite it aloud.

The proper references are to the General Rubrics of the Roman Missal 511-514:

IX - What Is to be said aloud and what quietly in the Mass
511. In a low Mass the following are said aloud:
a) the words In nomine Patris, etc.; the psalm Iudicda me, Deus, with its antiphon; the Confiteor and what follows up to the Oremus inclusive; but the prayers Aufer a nobis and Oramus te, Domine are said quietly;
b) the antiphon as the introit with its verse and the Gloria Patri, and the Kyrie, eleison;
c) the hymn Gloria in excelsis;
d) the Dominus vobiscum, Oremus, Flectamus genua, Levate, the collects;
e) the lessons, the epistle, the gradual, the tract, the Alleluia with its verse, the sequence and the gospel;
f) the creed;
g) the Dominus vobiscum, Oremus and the antiphon at the offertory, and the words Orate, fratres;
h) the preface and the Sanctus-Benedictus;
i) the words Nobis quoque peccatoribus; the Lord’s Prayer with its preface; the Per omnia saecula saeculorum and the Pax Domini sit semper vobiscum; the Agnus Dei, etc.; the words Domine, non sum dignus before the communion of the celebrating priest; the formulas at the communion of the faithful; the antiphon at the communion; the Dominus vobiscum and the post communions; and the words Humilitate capita vestra Deo and the prayer over the people;
j) the Ite, missa est or Benadicamus Domino or Requiescant in pace; the blessing and the last gospel.
The rest is said quietly.

512. The priest must take great care to pronounce the words that are to be spoken aloud distinctly and becomingly. He should not go so fast that he cannot pay attention to what he is reading, nor so slowly as to become tedious to his hearers. Nor, if he is celebrating at a secondary altar, should he raise his voice so as to disturb others who may happen to be celebrating in the same church at that time; nor should he lower it so much that he cannot be heard by those nearby. He must pronounce the words that are to be said quietly in such a way that he hears himself but is not heard by those nearby.

513. In a solemn Mass the celebrant:
a) sings: the Dominus vobiscum whenever it occurs, except in the verses after the Confiteor; the collects; the Oremus before the antiphon at the offertory; the Per omnia saecula saeculorum with the preface; the Per omnia saecula saeculorum with the Pater noster and its preface; the Per omnia saecula saeculorum with the Pax Domini;
b) begins in chant: the Gloria and the Credo, when they are to be said;
c) says aloud the formulas at the communion of the faithful and the words of the blessing at the end of the Mass;
d) says in a suitable voice the parts to which the sacred ministers are to respond;
e) says quietly the other words which are said aloud in a low Mass;
f) omits what is pronounced by the sacred ministers or by a lector.

514. In sung Masses, that is, those sung without sacred ministers, the celebrant must observe what has been said in the preceding section, and he must sing the parts proper to the sacred ministers. The epistle may be sung by a lector. If it is not sung by a lector, it will be satisfactory for the celebrant to read it without chant; the celebrant may, however, sing the epistle in the usual way.

The rubrics for the music are found largely in the Liber Usualis itself.

Follow-up question: Is there an official document like the General Rubrics that describes the specifics of the music at the EF? ... For instance, Psallite says that the offertory chant ends as soon as possible after Orate fratres; my pastor says the music must end well before it.

The latest music legislation for the EF is found in De Musica Sacra et Sacra Liturgia from 1958. At Sung Mass, "The singing should never last beyond the Secret." The Secret is said quietly and immediately follows the Orate Fratres, so it would seem that the advice given by Psallite is closer to the rubric than the advice given by the pastor.

On the other hand, it doesn't seem that the pastor would be exceeding his authority to restrict optional music during the allowed periods, as long as the proper Gregorian Offertory chant can be sung.