Probably depends on how much you are interested in getting your hands dirty. Since the sources are available, you could go and implement WebGL 2 rendering support to fix all the differences, but that can be a bit hardcore. 
One thing you could do is attempt to break down the different graphical mismatches into individual test case projects with more detail. For example the differences in text rendering (spacing, font size, etc.) don’t looks like they’d be explained by forward vs deferred alone. It is possible that there are individual bugs that contribute to some of the differences, and that not all of it is due to the quality level. I can’t say for sure, but in any case, test builds & projects that zoom in on individual items at a time (rather than multiple discrepancies at a time) could be helpful for the UE4 developers directly to take a peek at. Sorry I don’t have a better help to offer here 
Btw, regarding the performance issues you mentioned, I did found three items which altogether cause about a 20-30% slowdown in UE4 HTML5 builds:
With these fixes HTML 5 builds get a nice performance improvement.
The last one will come in UE4 in a future version, although one can apply it directly to one’s local installation manually by editing src/library_gl.js in the UE4 source directory.