So it seems that brake fires only happen on hard surfaces. If you go into the overrun or off the side and bury your wheels, there's no oxygen to sustain the fire. Something else to carefully consider in the building panic if there's no fire crew doing an effective job and the smoke and flames are increasing.
And the pax get a softer landing off the slides.
Then all you have to do is sell the chief pilot on your ex tempore brilliance while he's looking at a fat bill for pulling the a/c out of the mud and major structural repairs.