As a writer and editor, I read your editorial with great interest. However, I was surprised that you didn't provide the most obvious solution to making the example sentence gender-free.
Cast it entirely in the plural. "Those who drive without seat belts take their lives in their hands." This rendering satisfies feminists as well as traditional grammarians who rightly reject such neutered constructions as "chairperson" and "humankind."
By the way, that same day your paper let slip some other careless errors. One article contained this: "Third and perhaps most importantly . . ." ("Most important" is correct, "important" being an adjective rather than an adverb in this case.) Another story told of a journalist doing "a myriad of interviews." "Myriad" properly is an adjective, not a noun: "She has done myriad interviews."
One must be ever vigilant.
DAVID G. BOWMAN