I think beating out the rhythm would be a disaster.

It's essentially harmonized and accompanied chant.
Learn the melody and its contours first, let the other parts find their place in relation to that.

Agreed with Adam.
If the director was to become very familiar with the chant hymn decorated in this piece, and ask singers to do the same, things would quite easily fall into place.

Beside the rhythmic complexities, the harmonic language is pretty sophisticated. This is not easy music, but is it ever gorgeous!

Lovely piece.

I'd tell my choir: the eighth note is constant. Each measure is organized into groups of 2 or 3 eighths. I'll be conducting down-up for duples, and down-side-up for triples. Most of the groups are obvious. Some measures aren't as obvious, and this is how we'll do them:

measure 23: 2, 2, 3, 2, 2
measure 24: 3, 2, 3, 2
measure 36: 2, 3, 2
(etc.)

Mark your music as needed accordingly, using a small vertical stroke (ictus) on downbeats.

Watch me carefully in places like measure 8, where my beat will slow down on the second quarter, as if it were an eighth followed by an eighth rest. Note that there's a typo in measure 3, where the breath mark should be in the same place as in measure 8.

While I agree to get the even-eighth note idea down with your choir, as well as duple vs. triple figures, I would never think to beat the eighth note in this piece.

I think you misunderstand Chris's description. While the pulse or tactus is the eighth note, the real (down) beats he is describing are only on the beginning of each duple or triple, viz. down-up or down-side-up. And I would venture to say that the "side-up" part of the triple is not as pronounced as the "up" part of the duple; in fact, it is probably more akin to a rightward upward arc before the commencement of the next patterns (down) beat. There is no slavish ticking off of the one (up) or two (side-up) beats in this manner of conducting. Indeed, it is a sort of chironomy of its own.

To get the feel of it, use your own hand, making a distinct downbeat on "1" and arriving at the top before the next downbeat on "2" (for duple groups) or "3" (for triple groups) with such patterns these (the only distinct down beat should be on the boldface "1"):

1 2 1 2 1 2 1 2 1 2 1 2 (simple duple, e.g. 2/4, 3/4)
1 2 3 1 2 3 1 2 3 1 2 3 (simple triple, e.g. 3/8, 6/8)
1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 (5/8 = 2+3/8)
1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 (5/8 = 3+2/8)
1 2 1 2 3 1 2 1 2 1 2 3 1 2 (7/8= 2+3+2/8)
1 2 3 1 2 1 2 1 2 3 (10/8 = 3+2+2+3/8)
1 2 1 2 1 2 3 1 2 1 2 (11/8 = 2+2+3+2+2/8)

Make up your own patterns, being sure to use those found in the piece in question.

And practice, Practice, PRACTICE!

Conducting is not a matter of just keeping time with "beats" ... it is a matter of musical gesture that conveys the conductor's intent. Conducting this kind of music, as well as certain types of Spanish/Latin American types of music, is more like chironomy than conducting marches and waltzes.

For measure 23, as I suggested earlier, I'd use 2, 2, 3, 2, 2. The 2nd downbeat comes in the middle of the quarter. You might consider the quarter as 2 tied eighths, with the ictus on the 2nd eighth. Unlike in chant, where you sometimes see an ictus marked in the interior of a pressus, there's no repercussion. It's just for organizing the rhythm.