Our Very Catholic Choirmaster is a big fan of chant. We sing a LOT of chant - at almost every service.
His S.O.P. (which I think is very good) is if we sing a polyphonic anthem with a traditional text, first we sing the chant then lead into the anthem. There are tons of pairs that work extremely well this way - Ubi Caritas, the Magnificat (with any number of anthem settings), etc. etc.
I actually had to learn to read the Solesmes notation. . . . we're reading it off the original texts from the Liber Usualis (or the short version, Chants of the Church). . . and I found a copy of the short version for sale on line cheap cheap cheap.
And yes this is a VERY orthodox parish. Praise the Lord!
How much of your music is a capella?