Your video is disturbing. You show someone (apparently) signaling a left turn by raising their left arm with elbow bent at 90 degrees. The arm position means right turn but the glove light indicates left turn. Your video is promoting a turn signal convention that is opposite to the past century’s convention! This could endanger cyclists’ lives!
Your Q&A “Shouldn’t the arrow point toward the knuckles?” isn’t really answered. I don’t buy “Furthermore, having the arrow position in our product allows you signal in front of you without having to take your hands off the handle bars!” as drivers to my left will have a poor view of my right hand, when it is on the handlebars.
You should encourage people to signal in a manner consistent with existing conventions, not opposite to them! During daylight when the lights are less visible, or when the lights are viewed off-axis from their peak brightness orientation, what the cyclist intends to signal and what the car driver perceives could be 180 degrees opposite.
The conversation could go like this: “You signaled right but then you turned left! Why did you do that? … No, that’s not how you signal left! You signal left by sticking your left arm out straight, not bent!”
Retroreflectivity is hard to beat for visibility level when cars are around (which is also when it matters). So a little tape cut into the shape of any arrow + a little sewing takes care of the low tech / low cost end from my standpoint. At least that’s my plan when I start riding in the dark again.
The only scenario it doesn’t cover is needing to merge left while really pounding on the peddles so taking hands off is awkward and maybe dangerous.
I’ve thought about handlebar mounted turn signals before in that context, actually bought something very much like the brake turn signal combo at one point. It’s not a bad idea but I can’t say it stood out that much from the rear, it didn’t address visibility from the front at all and the useability factor was lacking… the switch could only be located on a bare part of the handlebar and it was awfully sticky so you just couldn’t use the thing without taking a hand off and applying force making you wobble more than a regular hand signal would ever make you do… so it was totally counterproductive, but a very cheap experiment thankfully.
If the switch were a button used by the thumb in a normal hand position on the bar that would address the useability. For the visibility, if there were easy to mount leds flashers in front, and the lights were bigger/brighter in the back and there were alternate mounting options I think it could work well and be a nice addition to the everyday ride.