We could modify the fire patrol speeder and tank to have a sprayer that douses the bridge ties when they go over it after the train. Wouldn't take much as the water, tank, and pump are already there. Having wet ties should take care of 95% of any hot cinders if there are any.
John, you propose a viable remedy. Unfortunately the length and deck surface area of both the Lobato and the Cascade Trestles would require more water that can be hauled by typical speeder patrol vehicles.
A good alternative would be climb up the learning/technology curve a bit and utilize currently available COMPRESSED AIR FOAM SYSTEM equipment. There are several manufacturers who produce "skid mounted" units designed to fit into pick-up truck beds that would probably be well suited for a speeder trailer. The system utilizes a very low fraction of (.005) Class A firefighting foam concentrate that is a detergent like surfactent. By expanding the application volume with compressed air, the water quantity requirement is greatly reduced.
I would similarly offer that a boric acid additive might enhance the ignition resistance of the ties and timbers.
One concern about regular use of chemical assets would be potential environmental impact on the downstream watershed. This might not be a big issue as the chemicals involved are basically non-toxic and not used in large quantities.