Sounds like you need to make a custom allen wrench. That's probably the best way to get out the bad one too. Take the next size up, grind each edge until you have to hit it to go in. Is there room to put the socket on an impact driver? Impact drivers are the only way to go for phillips and allen fasteners.
Be sure the safest rule is that we should not dare to live in any scene in which we dare not die. ~Lewis Carroll~