The weird thing is that the other three came off just fine. A little wd-40 and they came right out. I'm pulling the rear out, so I will be able to get the axle on a bench to try drilling it out.

I sat there with the drill into the screw for a VERY long time, and there's a dimple in it.

 

Before you do any more drilling, is the broken bolt flush or slightly proud of the yoke? If so, try cutting a slot with a Dremel cutting disk and using a screwdriver. I think if you heat the daylights out of it will come right out, especially based on what you said above.

 

It's inset, not proud or flush. The first roughly 3 mils of the bolt sheared when the head did.

 

I don't know how to do this, but I'm willing to try?

Does anyone know what size bit this is? I'm not getting any results with anything else.

The bolt is currently drilled another 3 mm in. Don't know the exact size of the drilled hole, but it's about 3/4 the diameter of the bolt.

 

The suggestion for a left handed drill bit is a good one, though I admit have never heard of a left handed bit.
If you have it started with a bit 3/4 the diameter of the bolt, well, might be ok. You want it big enough to do it but small enough not to take out the threads in the yoke. Keep adding oil as you go and use a good sharp bit.

 

To drill and tap - hit your local hardware/lowes/home depot and they will have a drill and tap set (a drill bit of the correct size and the tap) or the tap will indicate the size drill bit to use. You drill the hole out with the drill bit then use the tap to cut new threads into the hole.

I'd use a left hand drill bit or easy out first - what you don't want is an imbalance in the yoke with one bolt being heavier than the rest.

You don't want to remove the yoke unless you have to. It's not as easy as just spinning the nut off and putting it back on. Check the procedure in the FSM, it requires a lot of torque measuring and if it's not done correctly it will screw up the diff.

 

If the drilling is becoming difficult/slow, it's a sign the bit is dull. Get a new bit and keep it oiled as you cut. Drilling metal is a slow and tedious process. There is a reason folks go to great lengths to NOT break bolts off.