I can take a gpx and put it onto my Garmin Edge 305, piece of the proverbial. I don't need to load it to an intermediary mapping site (like mapmyride, ridewithgps, etc) either, though obviously I can if I want.
I use either GPSbabel or GPS Prune to do it. I prefer the latter.
I suspect my Edge is on it's way out. It's taking longer and longer to find satellites, that's how my first one went and then I got a refurb to replace it. This time around, I'll look at other options, including the Bryton. Though, I must admit, my initial impression of the Bryton is not good. I gather you're reliant on their web site to load/unload data, and I'd not be keen on that.