Couple of ideas off the top of my head:
- piece of bent, stiff wire to try and bend the flange up a bit
- longer pop rivet. Start to set it just enough to stop it coming through the flange hole. Pull the flange up and then gradually continue setting so that the head is pulled towards the skin. Once it touches the skin, finish setting the rivet.
No idea how to get rid of the debris - I have a couple of places with swarf swimming around......