Many soggy days here have meant plenty of time to refine methods for easier paper removal from foam board. I found that my fingers didn’t appreciate rubbing the paper off when dealing with large pieces. When the foam board is made, I understand the paper backing is part of the manufacturing process. Removing the bond between the two should be the answer. I tried adding white vinegar at a quarter to one-cup water ratio, but this added to material cost and only had a minimal effect on softening the paper.

So I tried the hot shower method. After a couple of minutes the paper became blistered. I then let it drain for an hour and then re wet the board on both sides with warm water and again left it for an hour.
I was pleased to see only a minimal amount of warpage and longitudinal shrinkage
of about 2.0mm over 762mm (30 inches) sheet length. I had previously lost 5.0mm using the boiling water method! The 230mm width appeared to have lost nothing measurable.

So saving one’s fingers this time I used a wet scouring 4.00mm thick pad to remove the paper. Just an initial light rub in circular motions helped score the surface, then rinsing the pad using cold water to remove the trapped paper in the scourer, I repeated the procedure to the smooth surface of the foam board, then rinsed everything off again.
Once the foam board was wet, the actual paper removal took about 20 minutes.
Again depending on how large your pieces are the times would vary.

So to conclude I would say for me this method is definitely easier than boiling water, using chemicals or trying a heat gun (that shrinks the foam cells) to dry peel the paper coating on the foam board that is available to me here in New Zealand.