Since we're all "That Idiot" to somebody anyways, might as well not worry about it.
Leaves the HR firewall. You undermine that by having somebody on the inside refer you. Or by having a work history that gets you in the door (which, of course, has a bootstrap problem). Or by working on OSS in that field. In other words: Anything that makes you stand out positively from all the other average programmers.
Is there a way to do this without knowing someone who can get you through the HR firewall, then being known as "That Idiot" until you figure it out?
EDIT: Difficulty, you must be an average programmer. Linus could probably get a job wherever.