Lambillotte, for sure.

Widor might not be most known for choral works, but he wrote sacred choral music in addition to the organ works for which he’s probably best known, and he and Franck have dueling views on the use of the organ at Mass (in a way: I remember from @kevinf that Tournemire and Widor had a tough relationship over the improvisations that Franck favored but not so much Widor).

Sticking to organ, and if you want to get into the weeds: there are a few recordings of Henri Potiron’s works for organ on YouTube, and I think that they are very serviceable, but more importantly, I think that while he tries to escape Romantic tonality, he’s not entirely successful (including in his Gregorian accompaniment) despite the peak of his career coming after Tournemire died, and indeed his entire life being after the Romantic era closes (but not its pedagogical influence) — at the very least I think it’s important to note how long this influence lasted, almost a century, even when you start to move onto other things (just in France: Tournemire, then Alain, Demessieux, Messiaen, Hakim, et al.)

@davido That is helpful. We do sing chant as well, so including Solesmes is a good idea. Also, making the connection between liturgical music and world events (impact of the French Revolution?) might be useful.

Wow! Tricky question, because this is the place where the history of liturgical music really diverges from classical music and becomes its own timeline.

There are two major traditions:
German: Michael Haydn -> J.C. Aiblinger ->Caecilians (Witt, Haberl, many others) ->post-Caecilians (Bruckner, Rheinberger). Reform-minded, inspired by early music. Post-Caecilians have 1 foot in Caecilian aesthetics while adopting contemporary techniques (and are successful in non-liturgical music). Caecelianism symbolically ends when Peter Griesbacher adopts Wagnerian harmony.

French:closer in style to the classical mainstream, though Gounod in particular was influenced (when he wanted to be, lol!) by Renaissance polyphony. Gounod, Saint-Saens, Faure, Franck. Many works for 1-3 voices for amateurs. Ends around 1905 with the French secularization law which cuts off the money stream to churches. (E.g., Vierne was never able to mount a performance of his Messe Solemnelle after that date.)

Other nations not important. Poland (Moritz Brosig,Max Filke) and the Austro-Hungarian states are in the German camp, the Low Countries in the French. England has just relegalized Catholicism and there are really no important Catholic composers until Elgar at the very end (not much liturgical music, and none really after TLS, but Dream of Gerontius is shocking for being an explicitly Catholic oratorio in a Protestant country). In Italy there's the last gasps of the old Roman tradition in Baini, but the style is mostly operatic until Perosi's school in the 1890s are inspired by the Caecilians.

Two important trends:
Revival of Gregorian Chant, in both major camps, just different texts (Medicean vs. Solesmes revival) though Michael Hermesdorff is doing a solesmian thing in Trier. Possible classroom exercise: Do a chant they know in the version they know, and then in a Medicean version.

Composers in Catholic cultures increasingly writing sacred music for the concert hall instead of the church, especially, if their own faith praxis is lax. Beethoven, Berlioz, Liszt (not lax), Gounod (ditto), Verdi. They could feel free to use all the tools at their disposal without the style strictures of liturgical music. Also: Catholic courts are drying up as music patrons; there's less money around for complex music.

Somebody needs to write a Catholic Grout!

Schubert & Fauré covers a similar wide span to your Vivaldi/Mozart pair. If plainchant is to be a theme though, Liszt's Te Deum (or Via Crucis in a Spring semester) might be useful.

One 19th-century thing to note, that began with the Anglicans and spilled over into Catholicism, thanks to soon-to be Doctor John Henry Newman: the Oxford Movement. This movement gave us many English translations of Latin hymns, mostly from the Office, and influenced the "high church" aspect of Anglicanism, thus, composers like Stanford, Parry, et al., and with "The Dream of Gerontius," Elgar.

I absolutely love Liszt's Ave verum Corpus. It unfolds very slowly and is gently chromatic, with some subtle surprises. It's got a minimalist organ accompaniment (which is very helpful in the tricky spots!), but it also works well a cappella (if your sopranos can find the E-natural in m.31).

Take a listen here.

I'm not sure I want to become the Catholic Grout!

Like fat-free food, Grout is dry and unappetizing. But its fat-free-ness is what makes it what it is. Whenever I see a highlighted Grout, I think "Why? It's ALL important."

I was wondering why I was only coming up with German and French composers, and you explained it beautifully.

It's mostly that only in France and Germany were there composers working in both concert and liturgical music. Musicologists in general aren't interested in 19th century liturgical music because the Church was no longer the driver of musical innovation. Catholic musicologists shy away from it because of the post-Caecilian/TLS privileging of the Counterreformation style. I'm the weird guy who thinks that any praise of Our Lord is worth study (if not performance), no matter the style. I've heard a fair bit of 19th century. Italian sacred music, but nothing impressive. Bellini's sacred music has its charms. But if the choice is between Temu Donizetti and Temu Palestrina, then the choice is easy.

Brosig was a Cecilianist and then he wasn't. Silesia was technically German during his life. I can talk your ear off about him ;)