Yes, that is a lot of wobble. I have seen that on the outer pulley (when the rubber disintegrated), but not the inner one.
The pulley #1 is also a harmonic balancer, so there is a rubber component to it. If that goes bad, you will see wobble.
As above said, the main crank nut needs to be checked. It should be on there with 362ft/lbs of torque, so a LOT.
Here is what I'd do (having pulled apart these engines often):
Take the nut off. You will need a long breaker bar with a 32 mm socket. If you put the truck in gear and make sure it does not roll, you will be able to do that. You can't get in there with an air wrench when the front clip is on. But a short 32 mm socket with a long breaker bar will work. Make sure it is at least a 3/4 inch breaker bar, or it will break.
You can then get the pulley off. First take pulley #2 off (6 12mm bolts, 18ft/lbs). Then tap on pulley #2 from the back and carefully lever it with a breaker bar until it comes off. It usually does not sit on the crank very strongly, so no puller required. Anyway, you cannot get in there with a puller with the front clip on. But be careful when levering the pulley off, as the front cover is aluminum.
Then look at the pulley. You should see if the rubber part of it is bad.
I doubt the key is the problem, as even a missing key will not allow wobbling. And I doubt the crank is bad, as it is massive.
Make sure to not lose the key, but usually it is stuck on the crank well.
Once you are there, you can replace the seal.
The one thing I cannot explain is the bad seal. Even with a bad rubber component of the pulley, the seal should not get mangled.
I do have a good used pulley in San Diego, if you need it. I might have a front seal too, but I am not sure about that.
you can pm me your phone number, if you want. I'll send you mine back...if you want to talk about this. As I said, we have rebuilt a number of these engines here, so a pretty good idea of them.
cheers,
Jan