I had this same thing happen on my 4.6, the drivers side bolt was fine but the passenger side one snapped exactly as you describe but a little further in
Screw extractor and drill ideas won't work unless you can find one that is like 4-6 inches long, plus the fact that the piece is solidly set in that it snapped to begin with makes it an almost lost cause
What I did was pull out the metal sleeve (it's a bitch to do but can be done with vice grips) I then tapped this out and used a 2" grade 8 bolt to hold it in making sure to set the metal tube with some epoxy to make sure it didn't move
Let everything dry for a good 24 hours and then bolted it all up again using, perfect repair
I've also heard of this, and drilling down the center of the remaining bolt, then using a screw extractor seems to be what most people end up doing. You can get longer screw extractor sets.. most are 3-4" anyway.