Hi,
Ok, I’ve made some progress.
Where I am with this is that I decided that first thing, I want a way to hook up any battery into the existing headlamp 3xAAA battery pack, without having to modify the headlamp. This way, I could move my mod to any 3xAAA headlamp.
So, I’ve made a crude “fake AAA battery extender” out of a small piece of wood, and to add the contacts, I used pieces of stripped and tinned wire:

To make that thing, I chopped up one of my wife’s largish chopsticks, so mine is bamboo, but any appropriately sized dowel can be used.
To make the contacts, for the positive end, I:
- Drilled a hole across the diameter of the “battery”, about 1/2” from the “front”
- Drilled another hole from the front, so that this hole met the diameter-wise hole
- Put a piece of tinned wire through the diameter-wise hole
- Looped a piece of tinned wire, where the “tail” was long enough to reach the wire that was going through the diameter-wise hole
- Shoved the “tail” of the looped wire down the front hole
- Shoved some solder wire down the same hole
- Using a soldering iron, heated up the diameter-wise wire
Heating the diameter-wise wire melted the solder wire that I’d shoved down the hole, so that created a joint between the diameter-wise wire and the looped wire (which was coming out the front)
I ohmed the wires, to make sure I had good conductivitity.
Then, I heated up the looped part of the wire, and melted some solder on it until it looked like the “nipple” on a normal battery.
For the back/negative contact, I did the same thing, but instead of making a nipple-type contact, it was more of a flat type contact to contact the negative spring.
After all of that, I had something that looked like a AAA battery, but with two wires coming out the side:


Comparing a dummy AAA battery to my fake AAA battery extender:

I ohmed all the contacts out, and after confirming that all was good, I tried it in one of the headlamps I have that normally takes 3xAAA by putting two dummy AAA batteries, plus my dummy AAA battery in it.
I then hooked up an 18650 battery to the fake battery “contacts”, and fired things up, and there was light - very bright light actually:

So, next I have to decide what to hook up to my fake AAA battery extender, then I’ll be done.
I have a bunch of 3xAA battery enclosures, but I’m still trying to find either a 1xAA or 1x18650 enclosure, because, while I could use the 3xAA enclosure with 1x14500 and 2 dummy AA batteries, I’d need to waste 2 dummy batteries.