Music for the rite of committal is covered in a bit more detail:
214. The singing of well-chosen music at the rite of committal can help the mourners as they face the reality of separation. At the rite of committal with final commendation, whenever possible, the song of farewell should be sung. In either form of the committal rite, a hymn or liturgical song that affirms hope in God’s mercy and in the resurrection of the dead is desirable at the conclusion of the rite.
215. In the absence of a parish minister, a friend or member of the family should lead those present in the rite of committal.
The minister should vest according to local custom.
The Song of Farewell is primary when part of the rite of committal, form 2, just as it is in the funeral liturgy. It’s good to have a sturdy setting that works a cappella just for the circumstance of singing at the interment.
We see that a concluding song–not part of the Order of Mass–is a strong consideration for any form of the committal rite.
What do you think about #215? It seems to prefer a lay person known to the mourners over a priest from another community.