I'm looking at a Corinthian helmet personally (inb4 not medieval reeeeeee!)
What thickness of Gambeson / Aketon were you looking at?
I'm not going for accuracy at the moment, just a Ran-Fest costume, so I'd make it out of the cheapest rough fabric I can buy. And I don't need the real thing, just something to get the look across.
Cotton Lawn should be a good alternative for Linen, depending on what you are looking for. Sailcloth is another good alternative for linen.
kettle helm gang, unite
I'll admit, those are some really nice looking helmets for the average solider.
Armets are the category where my personal favorite medieval helms fall.
Armets are a cool helm, I've always loved their small eye slits and general geometry.