Yes, I went the routing way. I am not 100% sure the thickness I ended up with. I started conservative, opting for it to be a little thicker just in case I made a mistake, and then routed away a little more and a little more till it fit.
The great thing about those volcano buttons is the button part does not have to stick up very far past the top of the cone to be usable. So that's what I ended up with and the thickness is just enough to hold.