Thanks for your comments!
We went through similar thought processes and experiments.
What we ended up doing (well, still working on it so jury’s out re quality of final result) is ditch the web embedding direction altogether and use the Discourse API to include full Discourse discussions inside our pages. This allows us to shape it exactly like we want, look-n-feel wise and much more. More work, absolutely, but it appears as if the final result is going to be worth it.