Trick with using the seal puller is hooking ONLY the seal, and pulling straight out, don't use the casing for leverage. Just get the corner of the seal and pull. I replaced the other axle seal yesterday, so now both front seals are done. Go figure 1 month after fixing one, the other one starts to leak =(
For the record, both sides look perfect metal wise, zero marks. That's with using jack stands and laying on the driveway. Just take your time and make sure you grab the seal and not the metal casing.
So a few pointers.
First off, if you jack up the car from one side only, you can easily do this job without losing any transmission oil. When you pop the axle out, nothing will come out, always better to left the car up evenly, but its nice to not have any fluid come out....
Without having a pin in the axle holding it to the axle stubs, you need to go at it differently than the OP. In order to get the axle out with ease, I'd recommend removing.
2 bolts on strut (MAKE SURE YOU MARK THE TOP ONE!!!!) put some touch up paint on it to mark it so you can put it back the same place (alignment issues)
Sway bar end bolt
Tie Rod End
Remove the ABS line
Remove the bolt holding the brake line onto the strut to give yourself extra room.
If you feel like it, remove the calipers but thats not really needed.
Once all of that is removed and the hub is just sitting in the Ball Joint, use a prybar to pop out the axle, takes very little effort to get it to pop out. Once it's out, lift up on the hub so the ball joint comes out and pull it away from the car about 3-4 inches until that axle falls down on the transmission side. Place the hub back into the ball Joint hole so it can stay there.
Remove/Replace seal, Pull the hub back out 2-3 inches and with your free hand line up the axle into the hole being VERY CAREFUL to slide it in smoothly, and place the hub back onto the control arm/ball joint hole.
The tricky part is getting enough leverage on the backside of the axle near the transmission to thrust it back into the transmission so it "clicks" back into place.
In hindsight, it might have been easier to remove the axle nut and just simply push the axle out of the hub VS holding up and pulling the hub from the car while directing the axle where to go with the free hand. But than you'd need another axle nut and would have to deal with breaking the darn axle nut free, sometimes they can be a total #@$$@#$ even with a pipe extension and all your body weight on it. Also when they pop, the tool can fall out of place landing on your wheels =( Not good if you have nice wheels.
The tie rod end, you can back the nut out so it's flush with the bolt and smack it with a hammer.
The ball joint is super easy to get out using
$29 from sears.
Cliff notes, if you have stubless axles, this job gets a good bit harder, but still doable. You just need to make A LOT more room to get the axle out.