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Is SIMD going to close that performance gap for a problem that otherwise fits well on a GPU? Wouldn't the ideal by WASM support for GPU access?

Indeed WASM supports GPU access through the normal JS WebGL API. Many asm.js/WebAssembly apps use the GPU in this way.

Though compiling WebAssembly to GPU code would be a very interesting thing to explore, too.

This probably won't buy you anything. The API you still have is WebGL, and JS is not the bottleneck.