(1) Don't let the US BCDW hear you say this! They would not agree at all with your interpretation of GIRM 391:
Nothing here about the diocesan bishop as far as regulating translations is concerned. And there was nothing in the US Appendix to the previous incarnations of GIRM either.
In the USA, we have "Adaptations" to the GIRM.In the dioceses of the United States of America, the following may also be sung in place of the psalm assigned in the Lectionary for Mass: either the proper or seasonal antiphon and Psalm from the Lectionary, as found either in the Roman Gradual, or, Simple Gradual or in another musical setting; or an antiphon and Psalm from another collection of the psalms and antiphons ; including psalms arranged in metrical form, providing that they have been approved by the United States Conference of Catholic Bishops or the diocesan Bishop. Songs or hymns may not be used in place of the Responsorial Psalm.
Furthermore, according to the Secretariat of Divine Worship at the USCCB, once a Diocesan Bishop has approved a "variant" Psalm translation, it can be used in ANY diocese of the USA.
(2) They are not interchangeable, and musical settings should reflect their different purposes.
I am not suggesting (and would never suggest) that a Responsorial Psalm should replace the Communion Proper.
However, in the USA, 99.99% of all parishes choose (abuse?) the "alius cantus aptus" option.
99.99% of the Parishes in the USA choose songs like "Eat This Bread," "One Bread, One Body," "Be Not Afraid," and "Be Not Afraid" to sing at Communion. Very few sing the Communion Antiphon as found in the Graduale Romanum
Much of the Psalter is very appropriate for Communion, and I would argue that singing Responsorial Psalms (especially with easy Antiphons that folks can remember and sing while in the Communion line) would be much better than "Eat This Bread," "One Bread, One Body," "Be Not Afraid," "Look Beyond The Bread You Eat," and the other Broadway Tunes that are sung during Communion at 95% of Parishes in the USA. Would you agree?
I, personally, have never done this, but I've seen it done at many parishes in the USA. Also, some Seminaries do this.
St. Antoine Daniel, pray for us!