OK, I am by NO MEANS claiming to have found the inventor but some diligent searching (ok, 15-20 minutes on google) and I found a recipe in the Calvary Baptist Temple (Savannah, GA), 1981 for a “WAFFLE MAKER OMELET” Recipe. 2 eggs, 1 cup grated cheese. Set waffle maker on high. Let cool on a rack. (ok, there is a bit more than that in the writeup but that is the gist of it.) CLEARLY that is 2x the standard default recipe.
Anyone find an earlier version? Waffle irons date to the 14th century and GE started selling electric ones in 1918. I believe the omelet precedes the waffle iron, but the likelihood that someone cooked an omelet in a waffle iron way before the keto craze is a near certainty. Just my $0.02