Does Hebrew moznayim, scales, derive from Hebrew ozen, ear?

One of the Torah proofs considered by BrooklynWolf in a recent post:

How does a person keep his/her balance?

Well, according modern science, the ear may hold the answer. "The inner ear includes both the organ of hearing (the cochlea) and a sense organ that is attuned to the effects of both gravity and motion (labyrinth or vestibular apparatus). The balance portion of the inner ear consists of three semi-circular canals and the vestibule." (Wikipedia, Ear)

Since Hebrew is a Holy Language, every word is self descriptive. The word "ear-אוזן" (Ozen) is of the same root as "balance-איזן" (Izun). The linguistic miracle of ancient Hebrew, proves its Divinity.

He points out that this is an instance of begging the question, and that if one does not assume Divine origin, then it might well be simple coincidence. See inside.

I recall where I heard this proof first, at a sheleshudes lecture at Etz Chaim from someone presenting evidence that the Hebrew language was of Divine origin. There were a bunch of similar proofs, about the orthography of ktav Ashurit and the phonology association with Hirschian Hebrew etymology. I did not find it very convincing, but left it alone.

Assuming that Hebrew was the first language, and no words were borrowed from other language, it does make sense that each root would be used to convey one and only one meaning. After all, if one wants to convey a different meaning, there are plenty of other three letter permutations available. I don't believe every three-letter combination is used.

However, before leaping to the conclusion that there was a deep knowledge that the inner ear controls balance which led to the word מאזנים, and izun, I would first look to more straightforward explanations.

The two straightforward explanations are: (1) מאזנים, scales, took its name from a surface similarity to ears which appear like two ears on the side of the face, and izzun as "balance" derived from "scales";

or (2) there is a homonym here, since the Hebrew zayin sometimes corresponds to ancient zayin and sometimes to ancient dhaled. (This middle letter which sounds like the "th" in "either" was mapped in Hebrew to zayin and in Aramaic to daled, which is why we often see this Hebrew - Aramaic switch-off.)

In terms of the former, it turns out that I am not alone in this assumption:

IN STRONG'S:

'azan  a primitive root (rather identical with ''azan' (238)  to broaden out 
the ear (with the hand), i.e. (by implication) to listen:--give (perceive by 
the) ear, hear(-ken). 'azan: through the idea of scales of a balance  as if 
two ears)

In terms of the latter, the difficulty is that in Aramaic, both the word for "ear" and the word for "scales" is written with a daled. (Udneih for his ear; Modana for scale, though there is a variant of moznevan with a zayin in Aramaic.) Perhaps we can claim that there is some error, some transfer from one common word to the other.

But apparently, there is this distinction in Ugaritic:

In Ugaritic: in  M. Dietrich-O. Loretz- San-Martin, Die keilalphabetischen 
Texte aus Ugarit (Neukirchen-Vluyn, 1976), Text (KTU 1.3:IV.lf.) The word 
'udn (pl. 'udnm),is literally "ear,"  see also Caquot, André & Sznycer, 
Maurice. Ugaritic Religion. (State University Groningen; Leiden: E.J. Brill, 
1980.) Pl. VII-X, XVIII, XIX.
...

Meanwhile, in the world of the Ugaritic gods as among humans, the deities 
use balances for weighing. When it has been decided that the moon-god 
yarikhu will marry Nikkalu, the father of the bride places the standard of 
the balance (msb mznm), the mother of the bride places the scales the 
balance (kp mznm),and the sisters take care of the stone weights ('abn 
mznm). [mznm] is the cognate of BH mo'zn # 3976 root of 'zn cf. Arabic 
[MyzAn] balance root of [wzn]. In all three languages Ugaritic  B. Hebrew, 
and Arabic the medial letter is uniformly a zayn

Given that we do have an appearance of the zayin in one variant in Aramaic as well, it seems that this may indeed be the case. If so, we are dealing with a mere case of homonyms and homographs, not some deep insight into the role the inner ear plays in balance. We cannot then use this coincidence to prove the Divinity of the Hebrew language.