It was an odachi, which (usually) has a slightly deeper curve than a (typical) katana due to its longer length. My whole point is that it makes sense for the first sword to use the earliest available forging techniques. It also incorporates the "plowshares into swords" idea that came up during the podcast.
The issue of blade length is also a problem. Shorter swords like the khopesh and xiphos tend to be used by cultures for whom the spear is the primary weapon. A marked deviation from this is the Roman gladius. The Roman legions did not use a "spear" as a primary melee weapon, but a javelin for use as a ranged weapon. The differentiating factor here, I think, is the massive shield carried by the Roman legionary. It allows the soldier to get super-close to the enemy in a close-packed mass with his buddies.
The description of the first battle between the Feanorians and the forces of Morgoth does not seem to support this tactic. The Noldor do not use tried and true military tactics. How could they, as they've never waged war before. They seem to rely heavily on their superior ability and a fear aura effect that comes off them, affecting Morgoth's rank and file troops.
This indicated to me that they carry more individualistic weaponry, such as a longer sword, and perhaps a small shield, smaller than that used by the greek hoplites. Now the khopesh, as typically found, usually tops out at about 60 cm, or about 2 feet. This is due, mostly, to the limitations of bronze. Iron example of the sword did not survive to the present day, though we do know they existed. Iron, or steel weapons would certainly be able to maintain a longer length, even with relatively crude sword-making techniques. The curve allows for a forged bevel on the cutting edge without having to hammer down both sides (which tends to make the metal brittle without advanced techniques).