I say this as I'm not sure how one would say this (/@ L'@k air'/ or [@ 'l@k air']) and more importantly, how would it be treated grammatically ('leac oighir mór/mhór/móire/móra').

I've found the phrase 'leac mhór oighir' which suggests that it can be analyzed as two parts with the semantics of the slab component being held the more important

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

The adjective would agree with the first noun:
leac oighir mhór

/L'ak ejər' woːr/

a big piece of ice

if it agrees with the second, the meaning changes:
leac oighir mhóir = a piece of big ice (which doesn't mean anything )

leac mhór oighir sounds ok to me...

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

GRMA

'Big ice' doesn't mean anything? I can imagine it meaning something in American English, like if you were basejumping off icebergs, or the like.

Never assume that something is ungrammatical until you hear an American not say it (if you get my drift). When I used to teach English I would say that X or Y was not good English (like 'aircrafts' or 'furnitures') then a few days later some North american would come out with something counter indicative. An English friend of mine swears he hear "new informations have come to light" on a news programme in the States... It's like their semantics are simplifying down to simply countable nouns with a few 'concrete uncounables' such as water, sand etc but anything too abstract is being thought of as an object

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

Well one thing, "bound genitives" like this are really just a case of turning a noun into an adjective.

Typically if a noun is used an adjective like this it is the last adjective:

Muga láidir tae = A strong cup of tea.

In this case, assuming you want to say "a big piece of ice", then oighir is really
just functioning as an adjective on leac, no different to any other. Since Leac is
feminine all adjectives get lenited after it and we list adjectives formed from genitives
of nouns last:
Leac Mhór Oighir

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

How about oighear-leac?!

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

Béarlachas... That word order isn't natural in Modern Irish.

In Irish it would mean "ice of flat-stone" with a mistake (leac should be in the genitive in this case).

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Ba mhaith liom píosa beag oighir-leice i mo leann úill, lol!

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

That's just píosa oighir.

Leac oighir - is a whole sheet of ice - a slab of it, as it often naturally comes in slabs.

Maybe I'm a giant in a human's house and speaking their language, aware of the semantics of the tongue!

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

In Muga láidir tae, it is the "mug" that is "strong", correct?

How about the following?

Muga tae can be either a "mug of tea" (a mug containing tea ) OR a "mugful of tea" (a general unit of volume of the said beverage ) OR a "tea mug" (i.e., a vessel for the purpose of drinking tea or a similar beverage but not necessarily containing any of the said beverage at the present moment ).

Muga láidir tae "a strong mug of tea" (i.e., the mug is strong and the tea may or may not be strong ) OR "a strong tea mug" (i.e., a strong vessel for the purpose of drinking tea or a similar beverage but not necessarily containing any of the said beverage at the present moment ).

Muga tae láidir "a mug of strong tea" (i.e., the tea is strong, not necessarily the mug ) (but may also mean "a strong tea mug" as above depending on context )

Would the above be correct?

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WARNING: Intermediate speaker - await further opinions, corrections and adjustments before acting on my advice.
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), agus Gaeilge an Chaighdeáin Oifigiúil (CO).