As far as a coule of different types of EZ-outs go.....
They all dig in further as you try to remove the screw. If you just stripped out the allen hex, you should be able to get an extractor in there and try it without drilling.
May I suggest that you DON'T get the generic extractors that are sold by like Sears and such. These models are approx 3" long and there are usually 4-5 in a set. The problem with them is they are very tapered and long. To get to the size that you need, it might be in the middle of the shaft. That would mean that you have to have a hole behind it long enough to get it to fit in proper.
HANSON tools makes a nicer set. Each extractor is only about 1/4 to 3/8 inches long with a hex on the back side to fit a socket and rachet on. Each size hole has a specific bit to fit it.
I'm looking at a set in my tool box right now. it's a Hanson screw extractor set. 1/8 - 7/8 25 piece set. Hanson may also go by Irwin or Irwin Hanson. The part number of my kit is a 53227. I would think you might be able to get a supplier in your area to get you one bit only. I know they are covered under warranty and they can be purchased one at a time if needed. They have smaller sets as well. I wish I were closer and could help you out. I get to deal with FUBAR'd stuff on a daily basis. I know I could get it out for you.