Thank you all three for your help and thoughtful thorough answers!

To Séamus O’Neill: My source for the example sentences was the 2017 Caighdeán Oifigiúil. And thank you for your help!

To DJWebb: Thank you again for your time!

To Labhrás: Well explained! If you don’t mind my asking a follow up question, I’m a little confused about the role of the copula in “is fearr” and “is ceart” in these types of sentences: Usually the copula is used to move an element of the sentence to the front for emphasis, but these are at the end of the sentence. Plus it seems like a “double copula” sorta thing, since the copula is already part of “gur” earlier in the sentence. Am I right in thinking that this construction is a bit unusual? And would it be correct in your opinion (in these sentences) to use a superlative such as “is ciallmhaire” instead of “is fearr” or “is ceart”?

I understood it to mean: it would be better for him to be there. Did I misunderstand it? I must have typed the long r by accident, but I don't know what I pressed to get that.

I think the is feárr is a relative copula. "the thing that is better".

It is a copula sentence.
The normal sentence (without fronting) is:
Is fearr liom é a bhailiú. = I prefer to collect it. (lit. is better with-me it to collect)
Is fearr dom é a bhailiú. = I should better collect it. (lit. is better to-me it to collect)
Impersonalised (without liom or dom):
Is fearr é a bhailiú. = It is better to collect it.

The copula is often used for fronting. The result is a cleft sentence. (is ... a verb)
But this is not the case in the sentences above.

But of course fronting can occur in copula sentences themselves as well. The result is again a cleft sentence.
Is é a bhailiú is fearr (liom). = To collect it, that is what I prefer / what is better/best.
Here are two copulas: First copula due to fronting, second copula is the original "verb" of the sentence, now in its direct relative form. It is at the end of the whole sentence because it is the rest of the original sentence after fronting.

And this sentence can be made a go (here: gur) clause:
(Deirim) gur é a bhailiú is fearr liom = (I say) that to collect it, that is what I prefer.

(David is right that there are more idiomatic constructions in Irish to say the same and which are preferred by native speakers. At least such cleft sentences with "gur é a" are very scarce.
Why they are scarce I could only guess.)

is ciallmhaire ...
That is only a "superlative" due to the formation of the rest of the sentence, as well as "is fearr".
Otherwise it is a comparative.
There are copula sentences as:
Is ciallmhaire Pól ná Síle. = Pól is more sensible than Síle.
Of course there could be fronting:
Is é Pól is ciallmhaire ná Síle. = It’s Pól who is more sensible than Síle.

In a sentence as above with a verbal noun component, the verb bí would rather occur (Tá sé níos ciallmhaire é a bhailiú.)
Here "is fearr" and especially more modal-verb-like forms as "is fearr liom" are petrified in their copula sentence structure.

What about with "sin mar"?

Sḯleann sí gur é ' bheith ann, sin mar is feárr é?

[Any positive/negative comments on natural idiom welcome]

I would doubt the grammaticality of this sentence.
"gur é a bheith ann" lacks a subject.
(sin mar ... is rather an independent addendum than part of the sentence)

If that's what it means, than the second é would make sense. Though I would expect a pause if there were a second pronoun: síleann sé gur é ' bheith ann, is fearr é. Maybe Labhrás can conform.

Also, slightly off topic, pertaining to the quote I gave by Diarmuid Ó Sé, how do you think it would be treated if it was a first or second person pronoun, rather than a third person pronoun? Perhaps

Do dhriotháir is mé é

or

Do dhriotháir is mé mé

_________________
I'm an intermediate speaker of the Corca Dhuibhne dialect of Irish and also have knowledge on the old spelling
Soir gaċ síar, fé ḋeireaḋ thíar

This is from Ua Laoghaire's Gospels:

Ansan dubhairt a chómharsain agus na daoine a chonaic roimis sin é agus é a d'iarraidh déarca: Nách é seo <L 252> an fear a bhíodh 'n-a shuidhe ag lorg déarca? Agus dubhairt daoine: Isé é. Dubhairt daoine eile, ámhthach: Ní h-é é, ach is cosmhail leis é. Ach dubhairt an duine féin: Is mé é.

Go raibh míle míle maith agat, a Labhrás!

Just to be sure :

The following sentences would both be grammatically acceptable in your opinion?:

Measann sí gur é a sheachaint is ciallmhar. (She figures that it is wise to avoid it.)
Measann sí gur é a sheachaint is ciallmhaire. (She figures that it is wiser/wisest to avoid it.)

Thank you again for your time and help, a Chara!

Grammatically, yes.
But not idiomatically.

The copula is usually not used with adjectives in their basic (positive) form (ciallmhar), but bheith.
And, as I said, even in the comparative degree, bheith níos ciallmhaire would be preferred.
Furthermore "gur é a (verbal noun)" is (whysoever) rare.