The projector has a USB input for video? If it does have a USB input, chances are it's just for slide shows of jpg and ppt files, and also the odd firmware update.
Judging by the frame rate you get with live view over wifi into a mobile device, I can't imagine that side of the planned connection producing good results for video.
I'd have thought your best bet would be to find a projector with a HDMI input, and plug the 6D directly in. Some HDMI cables are longer than a couple of metres, and if you really want range, HDMI extenders over CAT5 allow for a range of up to 250m, and then there are optical and wireless extenders too if that's not flexible enough.