“…the Quenya word for “far” is “haiya”, not “haila”…”
— here

This…is pointedly not true. They both mean far, actually, but haíla indicates something that’s further beyond than haiya…

Aman haiya ná — Aman + far + it is –> “Aman is far (away from where we are now)”
Aman haíla ná — Aman + far beyond + it is –> “Aman is far, far beyond (where we are now)”

If you want to pick on something that Oonagh actually gets wrong, why not choose her sung pronunciations of ninya and tyelma in “Nan Úyë“? Hint: they aren’t three syllables! The LotR musical falls into the same trap, when Legolas sings nyérë as “nee-AIR-ray” in “Lothlórien“…it’s NYE~H-reh, Greenleaf! Tsk tsk, Sindarin nitwits…;P

(I must note here that this is not the fault of the actor remotely — nor even the songwriters! This is a dialect coach’s responsibility and should have been caught early…though I don’t actually know if there even was a dialect coach involved with the musical, to be honest, and Google is being unhelpful. I’m sure there was…)