The seal is a very snug fit into the housing. Take a long screwdriver and stick it in under the seal on the one end. Push back on the handle to put outward force on the seal, and work your way around if you need to. You can also hammer a screwdriver between the seal and housing and pry it out that way. Doesn't matter if you mangle the old seal, just try not to raise a divot on the housing.

 

Success! But ultimate failure

After much cursing, I tore and manged the old seal up enough to get grip on it with a pair of channel locks, which was what it took. Got the new seal in using an oversized axle nut to set it, got it all put back together, refilled the fluid... but it's still grinding! I guess that means the bearings are bad. I should have known when it was apart; there was way too much play in the pinion gear. I'm going to throw in the towel at this point and drive it to a mechanic, I think. She's not not dripping oil though, at least not yet.