This doesn't really do all that great a job; Leaflet doesn't really seem
to be equipped to do this well (or, more likely, I'm just not figuring
out how to do it!).
The hack with the extra container is necessary because the transform on
the `.leaflet-map-pane` element creates a new stacking context, which
messes up even `position: fixed`. I wasn't able to figure out a way to
get around this.
Written on an airplane without an internet connection, so per the XKCD
I'd link but can't, "my apparent IQ goes down like 30 points when
[I don't have docs handy; orig "Wikipedia is down"]"!
