Better H3 headlights.

[f5fstop]

100w bulbs push the limit of the 10 amp fuse (one for each headlamp). What people don't seem to understand is that generators fluctuate their output, and in the winter with all accessories on, it might drop to below 10 volts, if only for a split second.
The PCM which regulates the generator's output does not increase output instantaneously since this could shorten the life of the generator. (Ever notice how your lights may dim for a second when the brakes are applied?)
However, there are bulbs out there that draw 55/65W, but state they output the equivalent of 100W on the highbeam. Not sure if this is all that true.

I haven't checked, but I don't see why you couldn't cut the feed wire, run the headlamp side of the cut feed wire through a relay and power it directly off the battery. Just use the feedwire from the BCM to the relay to turn it on when the headlamps are turned on.
If the lights do not turn on then, you might have to install a resistor in the BCM wire to fake out the BCM into thinking there is a bulb on the other end. This might or might not be necessary. Not sure if the H3's BCM is designed to shut down the circuit if no resistance is sensed.