Hi there, this game looks pretty great!
I work at Mozilla on the Mixed Reality & VR team (https://mixedreality.mozilla.org/), working on WebVR (https://webvr.rocks/) and A-Frame (https://aframe.io/). We're working on the WebGL players for Unity/Unreal Engine to properly support the WebVR API (https://github.com/caseyyee/unity-webvr-export).
We'd be ecstatic and grateful if you're willing to share your game's source code with us — and my colleague and I will do all the hacking and experimenting.
We really want to be able to have good starting examples (and proof!) that with just a few button clicks, you can be loading your Unity/Unreal VR games directly from within your Web browser.
With your permission, we could also use your project as a case-study sample and share it as well on a few of our web sites.
Let me know if any of this sounds of interest to you. My email's cvan<at>mozilla<dot>com, or you can reach me on Twitter, @cvanw. Thank you very much!