I've never had this happen to me. Maybe it is because when I shoot with my phone, it tends to be short clips here and there, rarely more than a few minutes. I learned how to shoot with Hi8, so I prefer to edit in the camera and not do much post either.
Maybe you could build some kind of handle with a sun shield. Start with a selfie stick, don't extend it, and then make a thick paper hat to block the sun. You'll need to plan out your design to match how you like to shoot. I find this crafty stuff to be quite fun.
