While I haven't exhausted the topic of voice and vowel, another area that intersects with intonation is that of rhythm/ensemble. As I mentioned early on, poor (or excellent) intonation has many potential causes. That's why we have to diagnose correctly what the underlying problem is and help the singers solve it, rather than just saying, "You're out of tune!"
Because of the way that unified vowels affects intonation (see this earlier post), chords won't tune as well if the rhythm of the choir isn't crisp and together--because the vowels happen at different times and don't "line up" in such a way that all the overtones/partials line up as well.
There are two parts to this: understanding diction and that we don't really deal (technically) with words, but the sounds that make up words. "My country 'tis of thee" has five words, six syllables, but seven vowel sounds. The diphthong in the word, "my" means there are two vowels--if those vowels aren't together, the intonation won't line up either. This is the genesis of Fred Waring's "Tone Syllables" (if you've seen the old Shawnee Press editions, you know what I mean!). Robert Shaw was brought to New York by Waring to help prepare his new radio choir and Shaw certainly learned those lessons. To get the best diction, the best unification of vowel (and best unification of pitch), the choir has to be able to sing all the sounds precisely together. I remember watching/hearing the King's Singers in concert quite a few years ago from the first row, dead in front of them. The unanimity with which they closed through every single dipthong was amazing--you could literally see their mouths closing through the "oo" as the vanishing vowel of the diphthong "oh" exactly at the same time.
The second part of this fits with Shaw's development of the technique of count-singing. This is a way to get the ensemble (before they pronounce words) to find a precise rhythmic ensemble and sense of intonation (since they're all singing the same vowel: one-and-two-and-tee-and) at the same time. Once the choir moves from count-singing to text, each sound (not each word) has to fit precisely in place. Shaw said, "There is no such thing as good intonation between voice lines that do not arrive or quit their appointments upon mathematically precise, but effortless schedule."
Again, the level of your choir will determine how far you take this and how you choose to teach it, but without a good sense of rhythmic ensemble and being able to sing all the vowel sounds in a given phrase together, your choir will not sing as well in tune as they could. Building a technique/discipline (whether or not you use count-singing) of rhythmic ensemble and learning how to correctly sing all the different sounds in the words we pronounce will make a huge difference in not only diction and blend, but of intonation as well.
And when intonation in your choir seems to be fuzzy, ask yourself whether the rhythm and ensemble of your choir is fuzzy, too. Again, Robert Shaw (although probably paraphrased, since I'm doing this from memory--Howard Swan's chapter in Decker/Herford's Choral Conducting: A Symposium): good intonation and good rhythm make a pretty smooth couple.