Cecile Gertken, OSB (1902-2001) made English translations like you described. The attached PDF file has the ones for Ordinary Time.

I don't know who has the copyright now. You could ask St. Benedict's Monastery, St. Joseph, MN, which is where she once lived.

The Marian Antiphons can be found Englished starting on p.491 of Saint Dunstan's Plainsong Psalter (Lancelot Andrewes Press).
The volume includes the entire Psalter and the Canticles pointed for singing, and the Marian Anthems with their attendant collects, all in square notation - highly recommended for all Music Directors' libraries.

Here's a quick version which I threw together, which can't possibly be under copyright, because I just made it (and I allow anyone to use, adapt, or alter it in anyway they like besides malicious purposes).

First of all, English chant is a bit stupid in my opinion (with all due respect to the people who put great effort into doing it well). It's just not very effective to separate the melodies from the language that they were written for.

Second of all, I think in some ways it's a matter of opinion how good an English adaptation is, because different people will have different priorities. How important is being faithful to the exact meaning of the text? How important is keeping the same number of syllables? How important is it that the natural points of emphasis in the melody line up with the emphasis in the words? I'd estimate it's half objective, half subjective.

As a final note, I think vernacular is not very stable for something meant to be as long-lived as the Liturgy.

CGM, your version of 'Ave Regina Cælorum' strikes me as even nicer than the original in lingua latina!

Thank you all for your responses. Permit me to respond to some of the comments.

Lars: Yes. Instead of a "closing hymn", which typically becomes the cue for the "in-and-out" types to make a beeline for the door once Father clears their pew, we decided to introduce the seasonal Marian antiphons, sung after the St. Michael prayer is recited by all (while the priest, etc., move into formation for the recessional). The priest (and deacon when we have one) remain at the entrance to the sanctuary, facing the statue of Our Lady, and sing the majority of the antiphon before beginning to process out. This will be our practice going forward.

OMM: I understand that there are some who don't believe that there can be a plainchant equivalent for the English language, or that adaptations of Latin texts can be created without compromise either of the tune or the text. As I said in my O.P., our parish is exceedingly "Latin-phobic", which leaves us with very few options. To my mind, introducing the people to the sound of chant, either the original Gregorian melodies, or newly-created ones that model them, is an important first step. In a perfect world, we'd just do all Latin and be done with it. As it is, we live in a fallen world, dealing with people who have been fed illogical prejudices regarding our Tradition. Making the perfect the enemy of the good is never helpful or productive. In the fullness of time, the Pastor and I hope to move the people closer to the ideal, while gently and charitably educating them as to why we're doing this, and why it's important to our unique Catholic identity. I have a great deal of respect for those who have committed themselves to the project of creating an English language chant repertoire, in particular the work of Columba Kelly, OSB (of happy memory), and Samuel Weber, OSB, who both have presented a respectable body of work in this area.

An alternative to singing the chant would be to sing a paraphrase of the Marian antiphons to a hymn tune. Aristotle Esguerra has a pdf of all 4 of them floating around somewhere.
A way of avoiding the chant issue

I would note that every time it is asserted the chant and the vernacular are essentially, as it were, like oil and vinegar, that ultimately works in favor of the anti-chant side of things, rather than working in favor of chant. "Even chant proponents say we shouldn't bother with anything other than Latin chant, so let's just take chant off the table now."

@davido et al.: You may find those in this thread. Thanks for the mention.