Isn't it possible that some things are true, but can't be proven? Maybe you
are right that the quote says "the young woman" (or whatever it is
translated as) even if sometimes in Hebrew "the" is used differently. So,
why can't you just let this go. This is one argument that can't be proven
beyond a shadow of a doubt.
No matter what you say, people can still say that this was a double prophecy
that was fulfilled in Isaiah's time and again later, so the whole argument
you are making does not make any difference anyway. I guess the belief in
double prophecies is a religious belief and not a biblical Hebrew subject.
(I don't think any quotes in the Tanakh mention any prophecies being
fulfillled twice.)
I think you should let this go, and try some other angle on Isaiah 7:14.