Hi Chris,
I'm not an electronics expert or anything, however, i have played with and botched quite a few caving lights using various LEDs and have some constructive comments.
As I understand it, when using a standard bulb, the resistance across the element actually increases as it gets hotter. This stops the bulb from burning itself out immediately. However, with LEDs the resistance actually decreases, which allows it to draw more current, which in turn makes the LED just burn itself out, quite quickly. (I'm REALLY surprised yours has not done this, if not i'm sure you will notice that the colour of the LED has changed, and the light output has decreased, signs that the LED is killing itself.)
Therefore, it is standard practice to put a resistor in the circuit, which limits the current that the LED will draw. Here is a calculator to work out what size you need.
LED resistor calculator
When using this calculator you also need to take into account that a fully charged battery will be closer to 1.5v, rather than 1.2v, giving you an initial 9v ish, rather than 7.2v.
Also as you said, these LEDs get REALLY hot, so i personally would not run them at 800ma, because the heat build up on such a small heatsink would lead to it burning out after a small amount of time. Personally i would go for something closer to 350-400ma.
The problem running the LEDs like this is that the light output will decrease quite quickly (but it would be much more reliable than your setup). These high power LEDs really do prefer a constant current source, which as you said, requires some circuitry.
Here is an inexpensive circuit (20 of them costs ?9, so share them!). They would provide the 350ma constant current required, easily fit into the headset and would only require 3AA batteries rather than the 6AAs you are using. Also you could play with them so that your light used both switch positions in the oldham. One position to power one if these, giving 350ma to the LED and in the other position, two of these could be used to give the LED 700ma. However, doing this you do loose your backup bulb, but if done properly it shouldn't be as important as if you were using halogen bulbs. :-\
I hope that helped.