I'm still quite puzzled how it really happened that the case was stuck so hard in the chamber. Perhaps, in the beginning, you were banging too hard to move the case out and it got deformed? The other thing is that you're saying that "the action kept slamming forward". Does it mean that you were doing all this with the barelled action still in the stock and the bolt carrier and other parts in? I would advise to remove the barreled action from the stock and then do all the operations.
I don't think the stock is an issue, but the action should be stripped at a minimum. Unless he is putting the receiver in a proper vice block, I'd rather have the action screws and stock absorbing the hammering than the receiver hard on the floor.
When I read the threat title though, I was pretty sure the solution to fixing it would be to sell the SKS as a used firearm and then buy a different used SKS for about the same price.
I suspect the sticking is either due to case deformation during the chambering process, or roughness in the chamber significantly increasing the friction holding the case in place.
I had a new firearm where this was happening, and everyone thought it was over gas, but when I got the case out and looked at the chamber it looked like the reamer which cut the chamber was in very rough shape. Cleaning helped, but ultimately the chamber needed to be polished.
When the round fires, the case blows out to full shape of the chamber, and should contract enough to then be extracted, but if the shape of the chamber is rough, then the case might not be able to contract enough to clear the rough spots, and then would still have a lot of resistance to extraction.
If you don't have a heat gun, try playing with temperature. a hair dryer to the action for a few minutes to warm up it might help.