(Welp, I typed out a lovely long reply, and there was an emoji in my first sentence, and everything after that was just ignored by the software and thrown away. I’m tired, and ticked, so it will have to wait for another day.)

If there's a time when you could practice in church, practice without amplification. The conversational register of voice that amplification allows is a temptation to be resisted actively.

My choir and I have a running joke, that when I die, they will have "sing it like you say it" engraved on the back of my tombstone. This is a mantra that I live by, and I harp on it constantly.

1.) MODEL what you want the chanting to sound like. Demonstrate a nice, evenly chanted phrase, and then have them sing it back. Repeat as necessary until they get it. Discuss the concepts of evenness and flow, so they understand exactly what it is that you're aiming at.
2.) whenever you're singing through a psalm, if something odd jumps out to your ear, finish out the verse, and then go back, modeling again the weak point, and repeat the verse.
3.) it takes time. Do it every week, and give your choir a year for some semblance of mastery. Expect things to be slightly off whenever there is a new singer.

If you model, discuss when things go awry, and have them correct before moving on, the choir will develop a sense of groupthink about this. Groupsing, if you will. And over the course of time, you'll almost never have to discuss it, or if you do, a simple "sing it this way please [demo]" is all it takes, and you move on. After a while, your choir will sightread things in proper rhythm, and it's glorious.

I'm firmly convinced that almost anyone can become proficient at this. We all say the Pater or the Credo together in rhythm when speaking. You don't have to teach the congregation... they just do it. Singing the equivalent is not that much harder, at least not conceptually.

Thank you for this question. I've learned some good tips.
This is so frustrating and for some reason it's my lower singers (t+b) who really slow down, much more than the higher voice.

As English speakers, we are used to a language that is spoken with approximately equal times between the stressed syllables. If I understand right, Latin was not, classically, paced in that way; yet treating it in that way tends to be helpful for singers: it reminds us to stress some syllables and ease up on others, to keep a peaceful pace and avoid a mechanical, plodding sound.

they look to chant (on the occasions when they do look to it) to fill a particular musical niche that isn't otherwise filled: the slow, steady, serious niche.

This is a very interesting observation. I suspect you're on to something.

I also suspect this is one of the driving factors behind assuming that Latin is "penitential". It's only trotted out during Lent, and the chants that are sung are minor sounding and lugubrious. They do this specifically to make Lent feel serious. But, of course, this is a trap.

Just last week I was just modeling to a coworker how "Gaudete" sounds very minor and yet it is one of the most joyful chants in the whole repertoire. We really need to disabuse congregations of the notion that chant is "penitential". Part of the way to do that is not only singing chant when it is "slow, steady & serious".