Try twisting and sliding, slowly.<quoted text>
These magnets are so powerful that I am unable to slide them sideways. I have even tried smashing the stack against the edge of a table. I should have kept them separate.
I kid you not.
Check for superglue. You may have a prankster around.
If you have a spare disk you may try holding next to a joint and flipping polarity. You use one next to the joint of two to counter the force between the two. Will be a trick if they are that powerful.
You can't block a magnetic flux, but you can shunt it to weaken the effect on a particular location. You suck off its strength. You can do that.
You can also drill a hole the diameter of them in a block of wood, then make a lever anchored next to the hole to shear them off as you insert the stack at the joint, one by one. Say a piece of 8x8x1/1/2 with a foot or so of 1x2x12 anchored with a nail next to the hole. That will work.