Try custom grinding the next larger metric or standard allen wrench with a slight taper to each of the 6 sides. Gently tap it into the plug with a rubber mallet while turning the wrench counter clockwise. If that doesn't work, use a small center punch to punch a deep indentation in the flat portion of the top of the plug adjacent to one of the 'flats' of the hex. Then angle the center punch in the 'loosening' direction and gently drive it with a small hammer until it starts to break loose.
If none of this works, DO NOT drill the plug for an easy-out. The plug is too shallow, you'll drill through, and then you'll have high-carbon steel shavings in your nosedrive. If all this fails, clean the plug with alcohol or acetone (or methanol), dry it thoroughly, and then GRIND grooves around the right sized allen wrench. These grooves will make space for the next step to bind better. Mix up some JB Weld, and apply it in the grooves you put in the wrench, then put the wrench in the plug. If you do this, use the LONG end of the wrench, so you can turn it after the epoxy sets up. After it cures for at least 24 hours, you should be able to turn it out. Get a new plug either before or soon after you do this, unless you like the idea of a permanent handle in your plug!