If you write formal poetry successfully, you have everything technically you need to write hymns. Beyond that, all you need is to know and love the faith. Especially "know", since you don't want to inadvertently spread heresy.

Some points:
1. I don't care that supernumary syllables are the one thing that chant hymns and Breaking Bread have in common. Don't use them. On a related note, be very cautious with metric substitutions. Swapping a trochee for an iamb might seem like just the thing until you try to put it to a tune. If you're going to, try to do it in every stanza.
2. Avoid the historic "2nd person familiar", or, to name it as it came to be used "2nd person obsequious" (thee thou etc.)
3. Don't abuse word order to force a rhyme.I'm not saying "never abuse word order'; you might want to for other reasons. In a jam, it's better to use off/false/half rhyme than to do something obviously there for the rhyme. Good models for this: Kathy Pluth, Emily Dickinson. Rhyming dictionaries are useful.
4. Enjambment? If you're writing for the Anglican choral tradition, the sentence will get sung; otherwise, it will be the line, and there will be a big GASP in the middle of your thought. Not saying "don't", just be realistic.
5. It helps to have a tune going in your mind to write to.

Summary of above: you are the boss, not the words. If the words start taking over, pump whatever iron you need to in order to put the words in their place.

study the Hymnal 1940. the melodies and four-part harmonies are unsurpassed and the voice leading is impeccable.

TCJ,

While it's possible to write hymn texts without firm reference to music, it's much much harder to do so credibly. The OP could, if he wanted, take melodies from the Office hymns, and write his own sets of words, rather than write his own music as well.

Somehow confusion existed. To write hymns is (frequently) to write both words and music, nowadays.

Lyrics benefit from leaning towards the austere and spare.

I'll agree, and clarify:
Hymns are experienced in real time, which is not how people now generally experience poetry. (Digression on poetry and orality omitted.) And are experienced with the distraction? of music. Because of that...I wouldn't say "austere and spare", which means something else to me. But I'd have to say that denotative meaning needs to be clear, and sufficient to carry the text. This is not to say that there can't be connotative meaning, that the various layers of a good poem can't be there. But the hymn lyric has to work at first hearing, and poetry in general doesn't. For example, pace Jeff Ostrowski, the poems of Robert Southwell don't make good hymn texts.

You have to hold back on a few things. Don't write as densely or as cryptically. Know your Bible and Catholic teaching. Let a hymn tune run through your mind and write.

By singing them! -
as found in The English Hymnal
The Hymnal 1940
The Lumen Christi Hymnal,
The Catholic Hymn Book (English, Gracewing, pub.)

"That’s basically what they did with At the Lamb’s High Feast. It’s almost word for word from the translation in my Missal."

My guess is that it's the other way around, and your Missal took its translation almost word for word from Campbell's 1849 translation of Ad Regias Agni:

At the Lamb's High Feast we sing. By R. Campbell, written in 1849 [C. MSS.], and first printed in his collection commonly known as the St. Andrew's Hymnal, 1850, in 4 stanzas of 8 lines. In the original manuscripts the first two lines are added as a refrain to each verse, but are omitted in the printed text. Cooke and Denton's Hymnal was the first to bring it into prominent notice, although in an altered form which has been copied by many compilers. Its use exceeds that of all other translations of the "Ad Regias Agni" put together; being found in a more or less correct form, in the most important collections of the Church of England. Many of the alterations in Hymns Ancient & Modern, Church Hymns, Thring, and others date from Cooke and Denton's Hymnal, 1853, the Salisbury Hymn Book 1857, and others. Another arrangement of Campbell's text is, "To the Lamb's High Feast we press" given in Rev. Francis Pott's Collection, 1861, No. 90.

-- John Julian, Dictionary of Hymnology (1907)

I would recommend you read Anthony Esolen's "Real Music" as a guide to writing hymns for the church. Also the hymns of Fr. Faber, Fr. Caswall and others are readily available through the internet. Look for Faber's "Jesus and Mary" and Caswall's "Lyra Catholica" they are excellent guides for learning to write hymns. As a rule, know your Catechism and know the scriptures these are hallmarks of early hymn writers. For a good foundation consider writing hymns for school children that teach them the Catechism. Take the tenants of our faith and adapt them to hymns. Fr. Jeremiah Cummings one of America's first hymn writers did exactly this. You can learn a little about Fr. Cummings by visiting my HYMN OF THE MONTH write-up https://www.motherofmercycatholichymns.com/hail-virgin-of-virgins/