You are posting svg files, but it is in the Corel Draw section. I mention only to check that it is Draw we are talking about and not something else like Inkscape since you did not post cdr files. Maybe your just exporting as svg as the forum restricts some attachments.
I imported it into Draw and when I look at the disco ball it is all outlines,(stroke). Maybe that is your problem right there and the cutting software is ignoring the outline, (stroke,) which is reasonable in some ways.
Fist thing I did was convert all the outlines to curves, (path.) I noticed at the 4 poles of the ball, there are gaps. I changed those a bit. Some places still look a bit uneven, but not enough to really tell or matter in cutting I think.
After I converted the stroke to curves, I used the smart fill tool and clicked on each section. This gives you a different type of cutting path. If you just reversed what you weed you could get the same result. But here is what I have as an svg and cdr. I ignored the giant R. Maybe this is enough for you to figure out your own workflow.
https://dl.dropboxusercontent.com/u/34207516/dball.cdr
dball.svg