Doug, I continue to obsess a bit over this weird anomaly but this light might interest you:

https://www.aliexpress.com/item/32823244215.html

It's a 1AA plastic headlamp that claims to weigh 26g, presumably without battery. Lithium AA is 15g so it clocks in a bit heavier than the coin cell lights, but it uses the totally common AA cells which hold tremendously more energy than coin cells. It has red and white leds with low/medium/high modes, claims IPX5 water resistance, and is $3.65+shipping, making it pretty affordable for your kit. I'm sure you can work out an even better quantity deal.

I have no idea of its quality and wouldn't expect too much, of course. But my venerable 1AA Zebralight H50 weighed 16g without the battery or strap, and it was made of metal, so adding 10g for the strap I can believe this plastic light is the same weight. I might order one just to play around with it.

It would be great if they made a 1aaa version...