Where is this "almost a volt" that you are talking about ? At full charge, under load, the battery voltage will only be 3.8 volts within 10 seconds, so it only really starts with 0.5 volt differential. The other part that is not so obvious, is that the LED Vf is not a constant. It might take 3.3 volts to push 100 ma through one, but at 3.0 volts, it might still pass 50 - 75 ma, so it will go through a slow dimming, vs on / off failure with a low battery.
Try building up a proto on a piece of plywood (forget the flashlight body for now). Just mock up a battery, wiring, LED, and a few versions of drivers. Take some measurements with a volt meter around the circuit to see where your current really ends up at, and if you are happy with the setup.
The great thing about playing with LEDs is that they are so cheap, especially now. When I started playing with them, we were paying $50 / each for LEDs that produced under 200 lumens. I burned out more than one 'learning" about LEDs, now that was painful. Today a similar LED is around $1 /each. Its a hobby, time to get your feet wet and have some fun.
I am serious about one thing though - buy some sun glasses and consider to have a cardboard box around to help block some of the light.