This is what I came up with so far. The mirror overaly is not resolved yet but I have an idea. One of the difficulties is the 84/360. But that is how it would be resolved. In this case, I just snuck up on it by checking a mirror circle in the sketch. You should be able to constrain it to be perfect.
As for constant webbing and such, it will require significant sketch control but nothing that can't be done.
