There are a few ways to affect the order.
DXF Optimizer will rearrange the sequence to improve speed, but if you select center start it will begin with the shapes closest to the center and work it's way out. It won't always do the perimeter last though as it is just trying to minimize movement.
Another way, and perhaps the easiest in this situation is to use Inkscape and draw the border last. I took your image and converted it to vector in Inkscape, copied the border, deleted it and then pasted it back. So it was the last object. It will now cut it last.
I'm not sure if an FLV or animated GIF will work to show you the result but I will attach the DXF that you can run in the simulation to see the result for yourself. Do not use DXF Optimizer or it will change the sequence and break the "solution".