The wattage with LEDs isn't as important as the light output. LEDs don't behave like light bulbs, where the increase in power is directly related to the increase in light output, particularly when it comes to very high current LEDs, where appreciable power can be lost in the current limiting circuit. My array of 9 white LEDs actually consumes about 0.72 watts on a 36 volt supply, so isn't that far off the power you quoted. The LEDs themselves consume about 0.576 watts, with the difference being dissipated by the constant current regulator.
I think that you may have some of the units a bit mixed up in your examples, as 1500 amps is an exceedingly high current. My guess is that you mean 1500mA? This is over the absolute maximum rating for the standard Luxeon white LEDs, according to the spec sheet. They seem to be rated at 1000mA, where they give around 80 lumens. Are the ones you're referring to the higher rated 5027 K2 Star ones?
These are rated at about 1500mA nominal forward current, with a forward voltage drop of between 3 volts and 4.5 volts. and a light output of 130 lumens. This shows quite why the power rating isn't too good a measure for LEDs, as the variation in forward voltage gives a power variation at a constant 1500mA of from 4.5 watts to 6.75 watts,yet the light output will remain at around 130 lumens across that range, as it's dependent mainly on forward current.
Assuming that you want to use 3 series connected Luxeon K2 Star LEDs, which is a good choice for lots of light, then if you connect them in series you will need a constant current source that can deliver 1500mA, which is easy enough to build using an adjustable regulator chip and a single 1.2 ohm resistor. This will soak up a lot of power though and will need a heat sink. Assuming that your battery nominal voltage is 36 volts, then the complete array of three Luxeon K2 Star LEDs plus current source will consume 54 watts. Most of this will be in the constant current source, as it will be dissipating over 37 watts on it's own.
Comparing the light output efficiency of a such a Luxeon array to my array of nine 5mm white LEDs is interesting. Each of my LEDs gives about 2.5 lumens, so my whole array gives only 22.5 lumens, for a total power consumed of 0.72 watts on a 36 volt supply. The array of three Luxeon K2 Star LEDs, driven as described, will give about 390 lumens for a total power consumed of about 54 watts.
My array gives about 31.25 lumens per watt, the Luxeon array gives about 7.22 lumens per watt - not very efficient at all really.
It would seem that the best way to get good efficiency would be to use a very large array of cheap 5mm white LEDs. Ten or eleven paralleled arrays like mine would give pretty much the same light output as three standard Luxeon Star LEDs (the 80 lumen ones), yet would only consume 7 to 8 watts.
Thermal runaway can't easily happen if you use constant current drive, although unless the LED is cooled adequately it could still over heat. The star LEDs look to be fairly easy to cool, as they have a nice alloy backplate. Cooling the current regulator would be harder, as 37 watts is a lot of heat to get rid of in a small space.
The best way to drive these Luxeon Star type LEDs would seem to be with a switch mode current source. This would be much harder to design and build, but would probably increase the power efficiency a lot and reduce the heat dissipation requirement for the regulator. At a guess, it should be possible to build an 85% efficient switch mode, which would reduce both the regulator power dissipation and the current drawn from the battery pack by a fair amount. Unfortunately I don't know where you might buy an off-the-shelf regulator that would do the job, although I'm sure they must be available somewhere.
Jeremy