First I would staighten some of the edges up..as per my pic.

You can leave it as a seperate geo easily...just extrude the edges down a couple of wee times and whack a few edge loops in...it will then square off nicely and the components will work.

OR you arent snapping and merging verts properly?? IF you have any polyline meeting the area you have cutout..you need a corresponding one on the 2nd piece for it to snap. You cant have free/lazy verts around..it wont work.

If you have extracted correctly then thos verts from the body polyline should still be there..if not put some wee ones in with polysplit.

chhers bullet