Dude, that really sucks. There is zero chance you will drill the remainder of the bolt out. That is a hardened bolt (I believe grade 10 or 12). Not sure why you were wanting to remove the cross shaft, but I expect you're about to get a lot deeper into the diff than you planned. If I were in your shoes I would use a die grinder and grind thru the end of the cross shaft until you exposed the 'pin' end of the retainer bolt. Then I would rotate the diff and pull the shaft out the other way. That would allow you to pull the c-clips and push the axle shafts out. Then you could pull the carrier bearing caps off (mark them left/right & top/bottom) and don't lose track of the shims. Then you could get the diff carrier out and onto a bench to go after the rest of the bolt. I would expect a little heat from a torch and you could probably twist it out with some needle nose vice grips on the portion remaining.
But that's just my thought. Curious if others have any better/diff ideas.