I know this post is a few months old, but I just found it, and it's a good post and helped me find those stronger leds.
If a Li-ion can't take the current (seems obvious it can't, at least not a small li-ion like the 18650), then just use a high drain Li-poly!
The LiFePO although better with the current than regular Li-ions, just suck wen it comes to capacity and are no match for Li-poly.
Okay, I know what your going to say... they are rectangular!
I see two solutions:
1) Get a fatter bodied flashlight and stick it in there (UltraFire TH-1300L or Ultrafire MCD-WF-2000F, for example)
2) Make a square section barrel (get a piece of square section aluminum tubing. For the head connection get it welded to a suitable piece of circular section tubing and thread it, for the tail cap get an end cap sold for those square tubings. Then get the corners rounded off and for the final touch, get it chrome plated! 😛 ).
You can now get a RC airplane type li-poly that fits the tube, they will easily cope with those amps and much more.
No I didn't forget the cooling... no there is no way a normal flashlight head can dissipate enough heat, unless... you temporarily* forfeit waterproofness and stick a fan in it! Yes, make some radial fins on the heatsink and put a 20 x 20 x 10mm fan above it, drill some air intake and exit holes. * you can put a thin (don't worsen the heating) rubber sleeve around the head that you can move to cover the holes.
Okay, I hope you liked my wacky ideas! 😀
Send me a PM with some pics if you build this! 😉