The specialized class-D extinguisher materials are specifically for the burning active metals, especially lithium, which is the most reducing of them. The metal alkyls are quite different even though they react as readily with air as do metals. The metals in the case of alkyls are not as elemental, but as essentially ions, ie. inert. The carbon anion is very reactive with oxygen but releases about the same energy per oxygen atom as any ordinary organic compound. The active metals, as elements, produce much greater heat per oxygen atom (or mole of them) than carbon compounds. Smothering those with sand or lime should suffice. The alkylide ion reacts with hydrogen ion, water is a strong acid by comparison and thus vigorous, but it doesn’t become hydrogen in the process. A light alkylide will become a hydrocarbon vapor and ignite in air if auto-ignition temperature and limits of flammability happen to be co-incident.

Bretherick’s handbook has a very good summary on materials for extinguishing fires of the group 1 metals.