TeeDee and I carry a tool that he made for working on knots. It is a 6" length of 1/8" diameter stainless steel rod. Grind one end to a very dull point and polish it. An old fuel pump push rod works very well - stainless steel, the right length and diameter.
Then gently and with much patience insert the tool into the exterior loops and slowly and gently work the loops loose. As you do this you will notice which loop is closest to the exit from the knot. Then concentrate on that loop and make it bigger and bigger until you can pull the loop completely out. After doing this with 2 or 3 loops, the knot will be loosened up and will come apart very easily.
Getting the tool initially under 1 or more loops is the hardest part and requires the most patience and gentleness.
We have found that this works very well on Amsteel because the coating lets the rod slip under the loops well..
Be gentle and patient and you will eventually get the knot undone without damaging the rope.