There are some 10-segment LED bars that are affordable. That, plus a custom 3D printed light pipe might not be bad. But it would be green or red...LOL.
Would a 10-segment LED bar be considerably cheaper than ten white SMD LEDs? Or at least so much cheaper that the deviation from Schiit's usual white would be a worthwhile tradeoff?
I also wonder how much it would complicate production if one were to CNC a 300º 0.5 to 1.0mm wide arc into the top shell around the volume knob. With a custom-made light pipe behind it the ten LEDs could "fill" that arc from left to right according to the currently set volume. Kind of like a progress bar, but in the shape of a 300º arc around the volume knob. (Ten CNC-drilled holes around the knob would do as well, but a continuous arc might potentially look better and/or might be easier to see from a distance because more light can pass through the slit than through a hole.)
If the light bar is sufficiently translucent, it might even be enough for it to remain behind the metal, meaning it would not have to protrude into the slot itself to still be bright enough to be seen just fine in daylight. That would reduce the necessity for a perfect fit, making production and assembly a bit easier.
I would also play around with using PWM for the "highest" currently lit LED to have a form of smooth transition instead of just switching it from off to on once a certain value threshold is met. Let's say 10 LEDs are used to represent a volume range from 0.0 to 1.0, where 0.0 is fully attenuated and 1.0 represents maximum volume, each LED would represent a range of 0.1. Let's also say that the attenuator is currently set to 0.37. That would mean that the first three LEDs for that "progress bar arc" are fully lit, and the fourth is set to 70% brightness. This could provide an additional visual clue about the currently set volume level. Or it might look like utter crap. Or it might not really show up at all, depending on how much any given light pipe design would blur the area between the lit and unlit LEDs. Hard to tell without actually trying it out on a real-world, physical device.
Probably close to impossible with tops that will be powder coated, though. And I have a strong hunch that you can't CNC an already powder coated top shell without risking the coating to chip off.
I was also thinking about using a small stepper motor instead of a motorized pot or a rotary encoder. When turned manually, they produce a short pulse that could be measured and processed by a microcontroller. But you might need to implement some sort of protection circuitry to ensure that your TTL components will never see a pulse that goes above 5V, stepper motors are anything but cheap, and they don't produce a strong enough pulse to be detected reliably when the shaft is being turned too slowly. So even if you "calibrated" the knob's position during startup of the device, it would very soon drift from the "known" position when manually operated, essentially defeating the entire concept.
You also can't use a servo. They're noisy when they try to hold their position, and you can't operate them manually. At least not the ones that are small and cheap enough for this application.
You could also place a small DC toy motor right next to your pot and add a large gear to the pot's shaft and a small gear to the motor's shaft to make your own miniature motorized pot. But that feels kinda bonkers.
Weird that motorized pots that small don't exist off the shelf, I always prefer the simplest solution over something as complicated as all of the above.