Hi Kirk
I tried the smallest one out a set like this , it engaged quite well and I thought I have you now !
http://www.ebay.co.uk/itm/4-X-Speed-Out-Screw-Extractor-Drill-Bits-Guide-Broken-Damaged-Bolt-Remover-Set-/142130643712?hash=item2117a58300:g:LRYAAOSwZJBX~u-P
but it just chewed into the head even further. When that happened I decided to drill the whole screw out.
This worked for me , but I acknowledge I had some luck on my side as it could have easily gone very wrong.
That said I did it twice ?