You can say 'a Babylonian confusion of languages,' and it will certainly sound better than 'language tangle,' which, as New Yorker quite rightly suspects, is not idiomatic.
But the problem, as I pointed out in the previous thread related discussion: Babylonisches Sprachgewirr - Babylonian confu...
is that in English, hardly anyone will associate the word 'Babylonian' with language confusion anyway, so it will basically be meaningless and you might as well just leave the word out.
The word we do associate with a confusion of tongues is the old
word for Babylon: Babel, as in the Tower of Babel, which is how the traditional Bible story is referred to.
It exists also in lowercase as a figurative noun, so you could theoretically say 'a babel of languages,' but that's not very common.
The other option, 'babble,' is apparently not etymologically related to Babylon aka Babel, but it still might be the most familiar word.
Otherwise I think I would just leave it out and say 'confusion,' period. (And New Yorker is right again, 'confoundation' isn't a real word, and 'confound' in the sense of 'confuse' is near-obsolete anyway.)
I also would not use 'tongues'; in this sense it's now mainly only literary or poetic.