Well, Joseph, I see your point. And the Rudy Project Zyon Sailing Glasses might well work. You can get the add-on Laser lenses that have mirror coatings and come in black (well, it's semi-transparent black) and that allow only 12 percent light transmission. That's a pretty dark lens. The Zyons are not cheap at $250, but they're excellent glasses.
That said, I get a little nervous about recommending them. You're going to have the most intense sun exposure of your life on Denali, and it's no place to see of a piece of gear is "good enough." One or two days on Rainier and the Zyons don't quite cut it, no big deal. You'll live. Two or three weeks on Denali and if they don't work out you have problems.
The thing is, for real glacier glasses Julbo is the beginning and the end. That's interesting about the Nomads (starting at $70). Are the headaches caused by distortion in the lens or something? Because I think something like them is your best bet.
For instance, Julbo's Explorer XL glasses ($120) are real mountaineering glasses. They're tough, vented, and have mirrored lenses that block 95 percent of visible light, plus 100 percent of UV. They're similar to what I wore when I did the West Buttress several years a back, and believe me, even with heavy glacier glasses the light was intense. And Julbo's Micropores ($140) offer a more traditional wire-frame design, with a nose guard and side pieces.
So, I really recommend you get some specialized glasses. It's an expense, but not that big of one when you factor in the cost of climbing Denali. Check Opticus for good information on getting the right prescription lenses in your Julbos. They specialize in mountaineering applications.