I think a driver board for a flashlight as it might enable me to put small reflectors around and bounce some light sideways rather than having a single LED which is blocked by the joints at either end. At least, that's my thinking. Always open to learning!
I think this would be complicated, but a great choice to learn. One issue is, your lamp is currently 4xAA. 4x1.5V is 6V and higher when brand new. This is higher than the typical flashlight driver would be rated. If memory serve, for the
NANJG 105c, the AMC 7135 is rated at 6V and the MCU (ATTNY 13a) is 5.5V. You will need to switch to NiMH recharge, that would be 1.2V per cell but coming off the charger it could be > 1.6V per cell (6.6V) or more for a moment. The LED load should pull it down soon enough - just don't start with max brightness when batteries are fully charged. Better yet, make yourself a "pass through" by shorting one of the battery slots so you run 3xAA at 4.5V.
A driver board like the NANJG 105c is even a platform you can modify hardware-wise and software as well. You can of course modify the native firmware with custom firmware. That is a lot of learning you can do there. I use an Arduino NANO as the ISP for my NANJG 105c's.
For NANJG 105c, you can change how many AMC7135 you put on it to control the total current (each gives you 350mA, you can have up to 8 on the driver). The native firmware will give you brightness control.
Besides the AMC7135 count, you can even upgrade the MCU. When you get really ambitious, you can swap the ATTINY 13 to an ATTINY 85 with more programming space. The ATTINY 85 will fit on the NANJG 105c. You need to bend the pins a little, but it will fit. I have 1/2 dozen of them upgraded from ATTINY 13 to ATTINY 85. All programmed with custom firmware.
For LED, you can use multiple in parallel or choose a single LED like a Cree R5 T4 T5 T6 U2... They have angle probably wide enough for camping or head lamp. For single LED, expect to need additional heat sink for >350mA If you are
not putting it into a flashlight with aluminum housing. The tiny aluminum plate the emitter is soldered on is not adequate when without that flashlight housing as addition heat sink.
I've 3 running Cree XML2 (10W @ 169lm/Watt per spec) and some running XML T6. Their XML-G (6W @ 199lm/W) and the XML-E2 (3W @ 137lm/W) series are lower power good single LED solution. At least two are real Cree from Mouser, a few with a Chinese made compatibles (LightBright or some brand like that). The real Crees are brighter (using a lux meter to measure), but not much, just about 10% to 20%. So I use the much cheaper compatible ones for less demanding application (ie: the ones that doesn't leave the house and can double-up when I want it really bright).
If you want really wide, perhaps glue (with heat sink glue) three or four R series (older cheaper) or four E2 series onto a single aluminum plate.
The learning opportunity there is big, but complicated getting there. If you just want to start simple, string LEDs in series and put on a ballast resistor and start there. Next step would be shorting out a battery slot (4xAA to 3xAA), modify the number of LEDs and change the ballast, now it is suitable for a native un-modified flashlight driver like the NANJG 105c. Get two, now you can learn to program the other one while one serve as the working one... Next round, you have your custom firmware.