Thanks Jason for starting this thread. Hopefully it can act as a hub for collaborations on a variety of projects.
For an AKG style headband; I can't see the heat shrink sleeving or sheathing affecting the overall springiness of the metal rod used untorwardly. Not over such a long length, with relatively little deflection occurring.
For what metal to use and whether it should be heat treated. Heat treating something that shape, in a consistent manner, at home would be very difficult. 301 stainless spring steel would be a good choice, as it doesn't need heat treating and comes in many different diameters, including 2.5mm, which I feel is about the diameter AKG use. Grade 5 titanium is also an option, but would be harder to form.
I had a go at modelling up a headband similar to the rigid type you described:
It uses a wide piece of elasticated ribbon to provide the clamping force, but any of your suggestions could be used with minor alterations. All parts are printed except for the aluminium standoffs, plastic washers, screws and the elastic.
It's only a rough outline of what's possible currently, although I will make the files available soon, after a couple of small tweaks.
I feel a laminated printed headband is overkill. While a printed single-piece springy headband may not be as robust as other options; from my testing they stand up surprisingly well, so long as it's printed with each layer running the full length of the band that is.
Keeping the amount of flexing to a minimum, by tailoring the fit to one's specific requirements, should allow for a headband that may last decades and even if it doesn't last quite that long, printing a replacement is no great hardship.
I've never used Inventor, but I do use Solidworks and I would recommend it. Also for $99; that sounds like a bargain.