So I ended up taking my wheel up to "the Hub" in Long Beach and gave them a small donation for use of their tools. I was able to get both cones off. I over-tightened the cone I had removed enough to get the opposite cone removed. From that side, I was able to hammer the axle through. On one side - the bearing was frozen to the hub body. On the other side it was frozen to the axle - so the axle was only going to come out in one direction. I was able to get the ring seal off of both bearings though and the wheel turns much better now.
I realize this is definitely not an optimal situation, but the wheels were free, and it was just an exercise to see if they can be saved rather than recycled. Anyway, I think even in this state this wheel is better than my current front wheel.