Mr. Miyamoto stopped by Smosh Games to play a round of Mario Kart 8 and do a short interview. Mr. Miyamoto spoke about Star Fox on a couple occasions during the video.
6:24 - Takaya Imamura (Artwork Designer at Nintendo) is working closely with Mr. Miyamoto on the new Star Fox game. They worked together on the original Star Fox and F-Zero games for the SNES. Jokingly, Mr. Miyamoto explained the reason he did not win the Mario Kart races was because he has been spending all his time playing the new Star Fox.
13:34 - Star Fox Wii U will be playable at E3 2015. Having the two screens really works well for the gameplay. They plan to make the TV's image be more cinematic and cutscene-like, yet retaining full control of the action with the gamepad screen. (It's implied that looking around the cockpit is done by physically moving the gamepad, which is how many current Wii U games handle camera controls.)
Thanks to Kevin and GoNintendo for the heads up.