Well let me clarify. Ahaz, in a show of false piety, refused to ask for a sign from the Lord - effectively rejecting a sign from the Lord and rejecting any help from the Lord. He had made up his mind that he would trust in Assyria rather than Yahweh.
Allow me to further clarify what I think your position is:
1.) Isaiah 7 is a double prophecy, which means that the prophecy was fulfilled (for the first time) several hundreds of years before Christ. If you accept that the first fulfillment occurred in the next chapter, then it is certainly incorrect to take "virgin" from the text because the young lady is impregnated by Isaiah. And this nullifies the prophecy as far as Christ is concerned unless you feel that the vague word was deliberately chosen so that one meaning of the term would apply to one prophecy and another meaning would apply to another prophecy. Also, I am left wondering, assuming you reject Isaiah 8 as being relevant, when exactly the first fulfillment of the prophecy occurred.
2.) God allows or intends for the author of Matthew, whom you believe to be Matthew for no legitimate reason whatsoever, to read the incorrectly translated Septuagint and take Isaiah 7:14 to definitively refer to an actual virgin.
3.) In refusing to ask a sign, King Ahaz feigns loyalty to Jehovah for no apparent reason unless we infer that he values Isaiah's opinion of him. Perhaps because Isaiah was liked among the people? I need some explanation here because, as far as I know, kings only feign loyalty when bending the knee before a superior king. It's hard to come up with many reasons why a king would feel the need to carefully choose his words when talking to some that he is allowed to have executed for any reason. Failing an explanation on your part, all you're doing is psycho-analyzing a historical figure... I thought this is not allowed in historical analysis. But what do I know? I'm just a math guy.
4.) Because the prophecy says that the enemies of King Ahaz will be defeated before the child is old enough to know right from wrong, it logically follows that a child born 500 years in the future satisfies this condition. I never did catch your response when I remarked that this was obviously not the intent of the passage, nor did I see your response when I said that an ultra-technical reading of the Bible would produce a parade of undeniable factual falsehoods.
5.) You accept that there is absolutely zero evidence corroborating the virgin birth narrative. Please explain what the purpose was of the prophecy, then, since the prophecy does not guide anyone's actions, nor does it serve as a warning, nor does it serve as confirmation of anything since the prophesized event cannot be confirmed and was not even confirmed at the time (Mary gave no accounts of anything, firsthand or otherwise).
Am I accurately representing your position? Please clarify either way.