So how do I go about removing the pinion seal and the bearing from the front diff? I've taken everything else out of the third member, and all that's left in there is the pinion seal and the rear bearing.

Whack it !!!!

LOL, well the seal will pry out easy enough,
but the bearing race needs to be either pressed
out, or use a hammer and a punch to drive it out.

Start on one side, smack, then the other side, smack
back and forth until it's all the way out, be carefull not
to gouge the housing where the race fits or it will be
much harder to drive the new one back in.

Good Luck,
Wild

Thanks

One added note: Use a brass punch for those races. Less chance of damage to the parts and you.  

When I tapped out the pinion with a hammer after I removed the large nut on it, both bearing assemblies were knocked loose, the front one stayed on the pinion deal, but the back out came loose.

Knocking the pinion and bearings loose like that won't mess anything up, will it?

Nah! When I set up gears I give them a tap to be sure everything is seated as I'm torqueing everything upon assembly.

The bearing next to the pinion gear is a pressed
fit, the bearing next to the big nut is a slip fit,
the crush sleve goes in between to keep the torque
on both, and so the slip bearing stays put.

Brass punch is a good idea, but soft and will mushroom
out bad if the bearing races are really tight.

Wild