Try doing a Development build (in WebAssembly, not in asm.js), and then open the web page console after the page throws the exception, and see if you can locate a call stack of the exception in question. The callstack should be able to help pinpoint to the root cause of the issue.
If you are building UE4 manually from source, you may be able to workaround the issue (effectively hide it under the rug) by going to HTML5ToolChain.cs, and removing the line where it says about -s OUTLINING_LIMIT, and add a directive -s BINARYEN_TRAP_MODE=clamp there instead. This will not fix the problem, but can potentially make the build continue through even when the error occurs. (That might or might not work out well, depending on what the actual cause of the error turns out to be)