Good work indeed, even though the hypotheses about the development of the longsword and the circumstances around it are kind of questionable. I would rather think about the longsword (appeared ca. 1300), i.e. a more powerful one-hander as the initial answer to the introduction of plate elements into the suit of armor (first depiction of the coat of plates is dated to ca. 1250, but such armor became widspread not earlier than the late 13th - early 14th century). The added protection has allowed to use more powerful weapons, like the longsword or the poleaxe. On the other hand, one-handed swords that were effective against mail hauberks have became less and less useful against solid metal plates. Thus, need for more powerful sword has arisen, and the longsword was the answer for it.
Moreover, I guess the role of the longsword in the battles of the Hundred Years War is a bit exaggerated. I do believe that in Europe poleaxes, maces, and picks were the weapons of choice for a foot combat since mid-14th century while short thrusting one-handers were used in close quarters. Generally, the longsword still remains a paradoxical weapon for me: fast and powerful, capable of both thrusting and cutting and having an aesthetically appealing shape, it looks like an ultimate Medieval sword design, yet its battlefield use in the age of plate armor remains pretty questionable.