There is SO much more to the Keys than just Key West. In fact of all of the Keys, Key West is the lowest priority for my wife and I.
If you are very diligent and start well ahead of time, you *might* be able to patch together a number of nights at various state parks in the Keys. A fishing buddy and I did just that 5 years ago. We were constantly on the move, but pulled off a 30 day fishing adventure with very little planning ahead.
Your signature indicates boats - be sure to take one! A shallow draft boat with a wide beam is great for back country flats fishing.
(We've never been to Quartzite although we did stop by the Grand Canyon (and the Smokys) on our way home from the Keys very recently :-) A little detour on our way home to the DC area!)