Isaiah 7: Fulfilled by Hezekiah?

Some have argued that Hezekiah is the fulfillment of the various prophecies in Isa 7, which is a view I used to hold to. However, such is a chronological impossibility. Ahaz reigned sixteen years (2 Kgs 16:2; cf. 2 Chron 28:1) and was succeeded by his son Hezekiah who began ruling at the age of twenty-five (2 Kgs 18:1-2; cf. 2 Chron 29:1). The date of the prophecy to "the days of Ahaz . . . king of Judah" (Isa 7:1) presents a major chronological problem for this hypothesis. Even though Pekah was in the last three years of his reign when Ahaz too over the southern kingdom (2 Kgs 15:27; 16:1), Hezekiah would have been somewhere between nine and twelve years of age, so it would have been too late for Isaiah to have prophesied of his conception and birth or when he would start talking (see Isa 7:13-25).