I just ran into this situation today. I don't normally cook, but due to a nasty protracted cold, I bought (among other things) extra large eggs. I would bring them to boil, then set them aside. For 12 minutes. Boy, that was overdone. After some web searching, I found that I should set them aside for 5.5 minutes for runny yolks. That worked fine, but man were they hard to peel. For both 5.5 and 12 minutes, I would douse the eggs in cold water afterward to make them easier to handle and peel.
The difficulty in peeling suggests that the less cooked the egg, the harder to peel. This experiment was done with eggs from the same dozen. Odd thing is, I can't find mention of this on the web. On the contrary, I find the opposite claims. I wonder whether such a claim was based on a controlled experiment.
Barring any other egg boiling hacks, I had to boil them longer if I wanted easier peeling. I figure that one way to boil the whites longer without boiling the yolk as much longer (it is the whites that are in contact with the shell) is to put the eggs from the refrigerator directly into boiling water rather than bringing the eggs to a boil within the water. This is because of the temperature gradient between the egg interior versus the surface, which is minimal when the egg is brought to a boil.
Heck, if I kept the pot on the burner for maybe about half of the 5.5 minutes mentioned above for off-burner time, followed by cold water dousing, I would probably get a very well done whites, with hopefully runny yolks. I expect this because I'm maintaining the surface of the egg at boiling temperature, so there will be more heat diffusion into the egg, at least initially, which means more of a gradient. I will have to experiment. In any case, the more well done the surface of the egg, the easier it is to peel, according to the experiment thus far
Another thing that web search has revealed to be helpful is to add vinegar to the water. I have yet to try this.
2018-03-11 UPDATE: My experiments indicate that I can in fact cause the outside white to cook much more than the inner yolk, thus enabling easier peeling while maintaining a soft yolk. I placed the eggs directly into the water after it was brought to boil, and I kept the water on boil for four minutes. The outside yolk was indeed well done and easy to peel. The only problem is that I caused too much differentiation between the well done outside and the underdone inside. The inside was still quite wet. Next time, I will try five minutes of continuous boil, which should cook the outside even more, making it even easier to peel, while propagating more cooking into the yolk.
I came upon a realization, however. With a runny yolk, I really don't want to peel the egg. I want to lop off the top and spoon out the inside. So the whole question of peeling a (very) soft boiled egg is kind of moot for me. I will still conduct the 5-minute boil test out of scientific curiosity.
2018-03-31 update: Transferred eggs directly from fridge into already boiling water for 5.5 minutes before immersing them in cold water. Shell was easy to peel, and yolk was still quite running, though more cooked than previous attempt. I think 6 minutes boiling is the sweet spot for runny yolks. Again, my experiments have been with "extra large" eggs.