There's a bit of a slip in the area of the Milky Way: an estimated
diameter of 30 kPc means a radius of ~15 kPc, which gives an area of
about 700 million Pc^2 for the disk instead of 3 billion Pc^2.  The
factor of four doesn't appreciably affect the conclusion that Charted
Space is just a tiny fraction of the galaxy though.

As a side note to the calculation: if the maps were "full thickness"
then there should be hundreds of stars per hex, as our galaxy almost
certainly contains at least 200 billion stars.  If you count Charted
Space in terms of number of stars mapped instead of disk area, then it
is an even more microscopic fraction.