I don’t think this is a compelling argument.
This type of argument makes sense if - as is typically the case - you’re suggesting that one word evolved out of another word. In that case you would be looking for a strong similarity. In this case the word faygele was a pre-existing word - the suggestion is that it was chosen to connote gays because of a similarity to faggot. In such cases you don’t need the same level of similarity.
It just occurred to me that the first reply transliterated the Yiddish word is correctly. Just returning to that.
OP (perhaps) and others who have come across the word only as written, transliterated wrongly as it is in hed (“fagele[h]”) would more than likely gravitate to thinking the English “fag[got]” was more than likely the etymologically source.
And if said others were not of OP caliber, they wouldn’t even question that.
The first such post was post #2, which you yourself quoted. 
Yes, I realized that as my Golden Five Minutes ticked away. I was spouting off about oral and llterate modes of transmission and their traces in an example as good as the wham-bam of OP query->first post.
Back in the day such good example when found would be placed in a glass case and, well, spouted off upon.