That's exactly my problem as well. I have GearVR headset which fits seversal Samsung smartphones and it's really nice to play around (and it's cheap), but the only piece of software written for WebVR is Three.js module, which doesn't allow different scene presentation to each eye.
But maybe I'll get back to work on my hack. Some suggestions are here: https://stackoverflow.com/questions/53775620/webvr-update-sc...