It took a long time, but I finally found a pair of sunglasses that worked - and were CHEAP! You can read about them here: The Best (and cheapest) Riding Sunglasses
I never liked tinted faceshields on helmets. I sure don't want to ride around carrying multiple faceshields, and have to change them out depending on the time of day or brightness.
When I got my Arai Signet-X helmet last year, I saw that a flip-down sunshield was available. I thought that this was the solution! But the sunshield only covered the top half of the faceshield, purportedly to allow you to read the instruments - but this was still letting in far too much light for me.
I think I have finally found the solution.
The Signet-X, like so many other higher-end helmets, sports a Pinlock fog-resistant lens insert. This is a plastic lens that is installed on the inside of the faceshield:
The Pinlock insert has a silicone seal around the edge that seals it tightly, so that there is an air gap between the Pinlock lens and the inside of the faceshield. This prevents it from fogging up in colder temperatures. The helmet actually comes with one when new, and you install it yourself.
However, when I saw this new Pinlock sunshield, I knew I had found my answer: This is a standard Pinlock lens, but it is treated with a light-sensitive coating similar to a "Transitions" type eyeglass lens. When UV light from the sun hits the lens, it darkens. When the sun goes away, the lens goes completely clear. Finally - a solution to get rid of sunglasses! But would it work?

I ordered the sunshield from the manufacturer, Pinlock, in the Netherlands. I was unable to find it for sale anywhere except directly from Pinlock. It arrived here in the US 4 days after I placed my order. Each Pinlock lens is designed for a specific helmet faceshield, so you have to make sure you order the correct one for your helmet. Of course, you also have to make sure that your helmet's faceshield is compatible with Pinlock lenses.
The "Protectint" (Pinlock's trademarked name for the sun-reactive lens) is available in several tint colors. I selected a neutral grey.

The lens itself has a green protective layer on one side. This layer is left in place while the lens is being installed.

Once the lens is installed (spread open the faceshield, apply the lens, release the faceshield, make sure the seal is intact), the green protective layer is removed. As you can see, indoors, the lens is absolutely clear, there is no indication that it will become tinted in sunlight. It looks like a standard Pinlock lens.

Now the test. I set my DSLR camera to manual mode and set the shutter speed, ISO and aperture to a fixed value, so as to get a true representation of the progression of tint. I put a piece of white paper behind the faceshield. This first picture is after the helmet had been in direct sun for 2 seconds.

After 4 seconds:

After 8 seconds:

After 16 seconds:

After 20 seconds:

After 28 seconds:

After 34 seconds. I continued to take pictures after this, but measuring the tint in the images taken, it did not get any darker than it did in this 0:34 picture:

As you may have noticed, I had half of the faceshield covered in the sunlit pictures. Taking it indoors, I took the cover off and snapped a picture of the faceshield to try to get an indication of the amount of tint - however, in the few seconds between taking it indoors, setting it down, and taking this picture, the tint had already started to fade. The time it takes to fade to clear is very close to the amount of time it takes to darken: about 30 seconds. The hotter the temperature the slower the transition from clear-tint-clear. It was approximately 80 degrees when I took these pictures.

As a point of comparison, I put my everyday sunglasses next to the faceshield after it had been allowed to darken to full tint. The sunglasses are slightly, but not much darker - and these are relatively dark sunglasses.

So how does it work in the real world? Amazingly well! The amount of tint is just about right - if I were riding on a sunny day in the desert with white sand all around, I might want more, but for everyday riding in real-life conditions, it's just about perfect. The transition from clear to tint and back is not noticeable - you learn to ignore it completely, and it becomes a surprise when you lift your faceshield and realize that the world is brighter when you lift it up. Riding through a tunnel is a non-event - the tint is not dark enough that you can't see in darker environments.
Overall I give the Pinlock Protectint sun-reactive lens a giant thumbs-up. Highly recommended!