You already know about the modded KL1 head.
Here's another option that's probably not often, if ever, thought of...
Streamlight Scorpion LED head (assuming you want to stay LED, otherwise, the xenon head fits too). There's a few caveats to make this work...
1. You must use a 3.6/3.7V R123A.
2. A small ring of wire needs to be placed at the base ridge of the LED module to help the FB1 body make negative contact.
3. A small magnet or spacer (only about 1mm-1.5mm thick) at the bottom of the battery to help lift the battery up a tad for positive contact.
The stock Scorpion LED isn't uber bright...about 35-40 lumens. I changed the LED to a LuxIII TWOH and it's about 55-60 lumens now (rivals my Huntlight FT-01 LuxIII, maybe even a bit brighter). I'm waiting for my SSC P4 U-bin that I plan to drop in to really make it shine. Current is reasonable (about 650-700mA) so runtime is quite good. The head comes apart in 2pcs allowing the LED module (sealed) to come out. All you have to do is cut the plastic cross above the LED to access the leads and happy soldering. Not that hard and throws like crazy!
You can see a pic of it in my sig - "Vital Stream Scorpion-FB1".