Fortnightly, our schola sings the Psalm as set to a Psalm tone followed by verses in a fauxbourdon style. This technique gives us the best of all possible (possible in our parish) worlds in the ordinary form. We have a simple tone that the congregation can instantly sing and not feel ridiculous, and we also have the more elaborate verses that sample some of the feel and length of the Gradual verse that is originally intended to appear between the readings.
We are fortunate to have two people in our schola who totally dedicate themselves to this task: one writes the Psalm and one who digs up these fauxbourdon settings and sets the text to it in a way that matches the tone. I'm not aware of any published resource that does this, which is very unfortunate in many ways.
It works beautifully for us. Here is Psalm 146, which will will sing with our full workshop choir this coming Sunday.