Played in-browser and worked well. As a fellow browser-game-developer, I feel your pain. There's always unforeseen caveats with porting to WebGL. But also, similar to you, I just upgraded my project to a newer version of Unity and it fixed some weird bugs with the browser version of my game, Recolonizer.
In any case, good luck with your development, your game is really solid, you'll go far!