The axles have to be pushed toward the center to get the clips out of the recesses in the side gears, so a pick won't work for you. And you won't be able to get the torque tube/differential housing out without removing the axles. It's a big interlocking puzzle. That's why I suggested a torch to cut the spider shaft and get the spacer out of the way.
Good find on the spider gears. I suspect you'll be needing side gears as well. That's why I suggested tracking down a replacement axle.
It's possible there's something wedged in between the ring and pinion that's preventing it from moving. Maybe a BFH would help. Since the ring gear is toast already you can't hurt it anymore by beating the snot out of it to get it to turn.
Helps with the frustration level too.
