Something I've rarely mentioned when discussing this subject is the relationship of Japan's fictional robots and their history to that of America's fictional robots and their history. (This post is a significant exception.) After all, there have been many popular/good series, such as Heavy Gear, Exosquad, and BattleTech which were created in the USA which, if they show a strong anime/manga influence, still are distinctly "American," arbitrary as that term is.
The single most obvious link between those series and their Japanese counterparts can ultimately be summed up in a single word: Battletech.
Battletech was originally an American board game that rather blatantly drew from anime... to the point of directly ripping off images from Robotech and other series. Oops. Ultimately, those designs were dropped in favor of original ones to avoid the lawsuits that began piling up, and the game took on a life of its own. And it created a cross-influence between Japan and America, as the game was released in Japan.
Other than Transformers, I'd say that BattleTech is the single most important franchise connection between America and Japan in terms of that ephemeral subject called "mecha."
(A short post, I suppose, but it was coherent, wasn't it?)