Oh hon, I hear you, but I'm not sure you're hearing me!
I did know that English letter "J" did not exist in the Greek
There was no letter J anywhere in any language, English, Greek, Hebrew, Latin, Etruscan, etc.
where the letter "I" was used to represent the "j" sound, but did not have the little foot
There was no J sound either.
The letter J came to be just because someone wanted to make the letter "I" pretty. The sound J came into use eventually after there was a new letter.
The letter J and the sound J simply did not exist.
My understanding is that the Hebrew yodh is a "j", ... representing the "/j/" sound, pronounced in English as a "y".
The sound is as a "Y" because there was no "J" either as a letter or a sound. People have replaced all the transliterated Hebrew Y's with the new letter and sound J. Europeans who are much more culturally aware and understand much more than us Americans about linguistics still pronouce the new letter J most often as a Y sound. Johan Sebastian Bach, for example. The Hebrew theophoric name Yoseph, Yonathan, and Yeshua became Joseph, Jonathan and Joshua. There's a hint there—how are those theophoric? Yonathan is the modern spelling of a pronounced name which over time you might as well say became shorted by slurring. Originally it was Yehowanathan. The same as Yeshua was originally Yehowashua. It sounds nearly the same, and there is a specific technical term in linguistics for this, but I digress.
The sound of the letter J also violates what Yosephus noted about the divine name. It was made up of four VOWELS. YHWH and their sounds in Hebrew are vowels. Inserting the vowel points in Hebrew you are left with a unique name of all vowels.
The definition of the name also points us directly to the same witness, that they are pronounced as 'breath'. Hebrew vowels are letters which—while in our modern alphabet we may dictate that they are "constants"—are pronounced with unobstructed breath, like breathing. Making the J sound requires a sound which is not a Hebrew vowel 'breathing' sound. Say the name Yehowah out loud, you'll likely notice you never quite close your mouth, unless you're enunciating it in a funny way.
I suggest referencing any reputable dictionary on the letter J. If you grasp that it and it's sound didn't exist until recently, just about the same time as the name "Jehovah" was created by a Catholic monk, then you can start to understand that there's a merri-go-round in your understanding. It sounds like a "Y" because it is a Y, and never was nor ever will be a J. God's name predates the letter J many thousand years. The Watchtower loves to point out that Jehovah has been in use for many centuries. Compare many thousands to many centuries.
Next, check out the Freemasons who use the name (I imagine you know that they do not worship the same God as we do? Theirs is, at the highest degrees of Freemasonry, freely expressed as evil as opposed to good.):
Jehovah is, of all the significant words of Freemasonry, by far the most important. Reghellini very properly calls it "the basis of our dogma and of our mysteries." — Encyclopedia of Freemasonry: And Its Kindred Sciences
The name of God (El) was used in poetry in the inspired scriptures. That poetry is written in a rhythm which demonstrates for us that this name is a three syllable name. Thus, Yahweh and other two syllable variations do not support the poetry that David was adored by our Father for composing. Halleluyah!
Just like theophoric and theocratic refers to "god", "el" is a generic title for "god" too. Nebuchanazzar was a theophoric name.
Mischa'El (Michael), which means "Chosen of JAH."
Thus, it would be incorrect to say Michael means "Chosen of Yah (or Jah)" because it actually means "Chosen of God". Here's a list of theophoric names for you.
Why Yehowah, not Jehovah or Yahweh or other variations? A simple "hang man" version of understanding the pronuciation of the divine name. There are also references to books you may be interested in, for example a very old book you may read online which talks about Hebrew grammar and pronunciation.
You may be interested to know that I've conversed with renowned scholar Gerard Gertoux picking his brain on his research on the divine name, as well as have a personal study version of the scriptures (online, you can use too!) which uses the divine name in Hebrew as well as I've learned it to be properly transliterated and pronounced as His original Hebrew name. (Psalms 83:18)