No. I question whether "a good version in 3 voices" can even exist, given that the normative texture is 5 voices, and it expands to 9 at the end. If one can use an organ accompaniment, and is not too persnickety about voice leading and dissonance preparation, one could boil it down to SAB and not lose too much important detail. "The high C part" is a late-19th c. accretion, and in such an arrangement one might better default to 1770, even though in the popular mind "the high C part" IS the piece. If it can have a 4th voice, the Rockstro (high C) quartet is SSAB, so you can probably use it as-is.

Is your boss pressuring you to do this, or a soprano with a high C? You might want to explain to them that your program isn't ready to do this piece yet. There's no shame in prudence.

I understand the temptation though, In 2019, one of our priests was at a concert where it was done, and he said "You guys should totally do that". I knew it was a joke, but I can't take a joke. It's just a falsobordone; how hard can it be? Plenty hard, when even 4 voices is an utmost challenge. But we had 1770, and an organ, and didn't use a solo quartet, and grab whatever you want on the last verse, and we were set for Passion Sunday of 2020. And you remember what happened. We had to wait until 2025 to have the forces to do it even that way. This year I have a high C, and she wants to do it (why I'm considering it) but she's scared to do it (16...) and we need special rehearsal time. It might happen though.

However, dagnabbit, I'm being tempted to see if it can be done, as an academic exercise, and so it gets me to a confessional. If I do, I'll post it here for comments. This reminds me though about the cartoon about John Cage's 4'33" "arranged for beginning band. Duration: 2'00"

I got mine from CPDL.
Here's a boildown of 1770. I'm not nuts about the 3rd measure, but there's no way to manage the double suspension. With an organ playing the original, it wouldn't be as bad as doing it unaccompanied.

I have a 4 voice arr. with the high c if anyone wants it.

KF

Kevin, yes! I'd like to have it if you could provide it!

@kevinf I am also interested.

I admit this is a tangent: am curious about the thought process of wanting a reduction of such a well-known classic rather than choosing a setting of the text for which the array of one's choral forces is better matched. I know if I were in the pews, I'd be distracted more than edified (except perhaps to go into a compositional mental rabbit hole about the reduction choices) by that kind of reduction (I suspect less so if it were an instance of a very obscure work). I get that the Allegri is not full counterpoint of multiple melodic lines (thus, not like reducing Palestrina's Sicut Cervus to two lines), but leans more into a procession of chordal harmonies such that reduction is more possible.