Question: I'm using KiCAD to create a nested series of PCB rings - each two layer with copper fill on the front and back. The problem is when I add edge cuts defining the inner and outer edges of the outer ring, it removes the copper fill from the center area where I'm going to nest the inner ring.

Is there a way to add a nested copper fill area within the inside diameter of the outer ring and still maintain the edge clearance of the copper fill that the fab requires (ie, using the edge cuts layer, KiCAD automatically create a standoff so the copper doesn't go all the way to the edge of the cut, thus avoiding possible shorts).

Answer: 
KiCAD is an interesting animal - its a series of separate applications (Eeschema, Pcbnew, etc) that are launched and loosely integrated through a project management executable called KiCAD. When KiCAD launches these executables, it hides some of their built-in features. One of these features is within Pcbnew - the ability to append other PCB files to another PCB file.

If you launch the Pcbnew executable manually, you can create a new PCB file and append (file-menu Append menu item) other PCB files to it. In this way, you can create panelized PCB designs or in my case, create a nested ring design where the individual nested PCB's are electrically isolated.
KiCad only supports one board per file.

Optimal use of available space is up to the manufacturing house, they can tell whether it is possible to place small boards inside larger ones, because they know the size of the router head they use to separate the boards.

The alternative is to connect the boards, and define V-Grooves to separate the boards later. This could be more expensive to fabricate though, and concerns about the router head side still apply. For this, your board outline should be a single line, and the board should be connected still.