I've always used my Gemini Duo on a headstrap, and then when that died, a Yinding on the Gemini headstrap for running and skiing. I find I want as much light when running as biking (because its about seeing where you are going, not just the ground in front of you), and liked the two emitter systems to blend a narrow and wide optic. You can still get the headstrap style that works with o-ring mounts (see a Gemini version on action led).
I modified mine, deleting the overhead strap, eliminating the double run sections of strap (to reduce weight/bulk), flipping the mount upside down for better bracing angle on the forehead, padding the back of the mount, and sewing on an angled strap on the back of the head so the strap V outs into an upper section and lower section with battery pack. It's super comfortable and stable for running, more so than a much lighter, typical single 18650 L-shaped light because of the weight balanced between front and rear and the rigid plastic mount with a lot of surface area/bracing angle instead of small footprint, flimsy silicone.
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I do have an L-shaped 18650 light that I use now because the Yinding also died. Inexpensive choices are few now that most bike lights are battery and head combined. I tried 5 different optics in it to get the best compromise light profile with punch but also enough to see just in front of the feet. It's decent, but other than being more compact in the pocket, it doesn't give as good a light carpet from the feet to the distance.
For camping, maybe you would just need a wide angle light single 18650 light, but since you seem to want something powerful (hiking with route finding?), a bike light-based headlamp is more powerful. If you have money to spend, orienteering headlamps are similar and the designed for runners to use while racing through the woods on unfamiliar, untrailed terrain. I got my Duo/Yinding setup in part because I used to do a night orienteering race once a year. Lucifer M, LedX Snok, Lumonite Air2 are some 2 emitter lights kind of similar to the Duo and Yinding - other larger orienteering headlamps can go way more sustained lumens than that too.
