Seeing as anything falling from the aircraft will show up on radar, the solution will be that we forget the suicide note and he instead radios that his aircraft is starting to break up and pushes out a selection of spare parts before he pushes himself out (using a stolen rig). That should fox them for a while.
Another way is that he takes his rig and leaves it, upon landing after his 'emergency exit', in such a way that it looks like he did not fasten it correctly, so that at some point on the descent rig and occupant parted company. Authorities find rig, cannot find body but assume it is somewhere in sparsely populated area.
This is fiction, right?
