Shadow mapping in WebGL without WEBGL_depth_texture on Android devices?

Question

I wrote a web application that draws an interactive scene, including shadow mapping, using JavaScript and WebGL. I'd like to make sure that this site works on as many Android devices as reasonably possible. Shadow mapping works fine on desktop computers - both by using depth textures and by abuse a color texture to store the depth. But I haven't managed to make the site render the scene with shadow mapping on Android devices without major artifacts.

The problems are

1. According to webglstats.com, most Android devices do not support the WEBGL_depth_texture extension, so directly using the light source depth buffer as the shadow map does not work.
2. The workaround is to encode the depth of each fragment as a RGBA-value. While this works fine on desktop computers, the same code causes major artifacts on Android. My guess is that this is a precision issue: Either the precision of the WebGL-computed depth values is too low, and/or the floats in WebGL fragment shaders with mediump precision (According to the shader compiler error message on my Nexus 7 2012 Chrome, highp is not supported for fragment shaders) are actually only half floats and thus have a too low precision for splitting the depth value to RGBA values.

Are there working examples of WebGL shadow mapping that run fine on the majority of Android devices? Or is this just not reasonably possible? (Emulating a higher float accuracy through something like floating point expansions seems prohibitively expensive in a fragment shader).