Your instincts are correct, TCJ, avoid playing this on an organ (without a guitar or piano along or the ride), or even a simulacrum ;-) using an organ-like, string or pad voice.
Certain 3/4 or 6/8's can translate to organ alone, but this Haugen ain't one of 'em. If TPTB insist, I'd use tremulant as well and totally go for the merry-go-round effect, AKA mighty Wurlitzer. Maybe then they won't ask anymore.

When I have a hymn I can't easily do on organ (or if I have to do something on piano but hate the accompaniment), I usually just kind of fake-book it with the guitar chords and melody line. It's the only way I got through "Companions on the Journey" one harrowing time. I think that'll work here.

I can do it that way... it just irks me any time a pastor has an organist (something some churches would love to be able to afford) and doesn't really want one. Plus, it seems so cheap.

"Gather us in" has a similar problem. My solution to it, for what it's worth, was to play it on stops designed to make it sound as if we were in the court of Henry VIII.

There's another possibility: acknowledge that it's not written for organ, and is therefore badly played on it. Play what's there, persuasively demonstrating that it is designed for some other instrument. When congregations can't sing it when you play the accompaniment as written, propose to TPTB (as Charles calls them) that there are options, but playing it this way isn't the one they want. Then, the ball's in their court.

I tried this with a wretched piece called City of God. It starts almost sluggishly, as if waking from slumber. I didn't get a request for it, ever again.

I can't help with the original question, but the following may be of interest to some -

There is a beautiful and very simple setting of St Francis' canticle at no. 307 in The Hymnal 1940. The tune is Assisi, which is very chant-like, not at all unlike Jesu dulcis memoria, and just as easy! It is a verse translation by Howard Chandler Robbins. I recommend this to any and all. Children love it!

(Oh: it can be accompanied by the organ, but is really quite effective as an unaccompanied chant-like tune.)

The organist played the piece quite well on the organ, but the two eighth-sixteenth-dotted eighth measures in the refrain were each changed to 3 eighth notes, and some of the sixteenth notes in the verses were also changed to eighth notes. (The PIPs seemed to be accustomed to these changes.) This eliminated most of the "cutesy" elements I find in the piece.

While practicing it today, that's pretty much what I did. It'll work out. Since the congregation is completely unfamiliar with the piece, I don't think any of them will notice the changes. I'll probably be the only one singing anyway, even after several weeks of playing it.

Frankly, it's a rare congregation that sings those silly 16th-dotted 8ths (almost as rare as congregations that sing Be Not Afraid as written). I think I've heard it done "right" once (you need a really dry (think...carpeted) acoustic to pull it off convincingly.) I am totally in favor of disregarding compositional twaddle like that. (Just like I am totally in favor of congregations adding ornamentation to the final lines of Holy God We Praise Thy Name even when their printed resource doesn't - if only we could get congregations to reinsert Beethoven's anticipated rhythm in the bastardized version of the Ode to Joy that afflicts most (but not all) hymnals and all missalettes. Marty Haugen's twaddle is not the equal of Beethoven's; actually, Canticle of the Sun and the Ode to Joy would make good compare/contrasts in that regard.)

with 60 70 year old hippies

Fixed.