These may be difficult to find since traditionally the organ was not played at funerals - hence no (or very few) older pieces based on the Requiem mass chants. The possible exceptions are pieces based on the "Dies Irae" chant written for concert use, but these may be too long / loud for your purposes.
There are some pieces by more recent composers (copyrighted) - Gerald Near, Charles Callahan, and Dom Paul Benoit come to mind.
There are a few pieces based on chant melodys in a german publication by Johann Diebold from the turn of the century on IMSLP. He has several organ albums based on chant melodies, but one has a direct relationship to the requiem chants: The Catholic Organist at High Mass and Requiem.
Benoit's Triptyque pour orgue (pro defunctis) looks to be a late work, published in 1969. The three pieces are "Prelude au Subvenite," "Offertoire," and "In paradisum."
It is no longer in print in the US, but according to this website, it's still available through a European publisher.
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