Nice looking chondro. I would skip the wet pillow case and go with a tub setup, no perch, with moist paper towels as the substrate. If the skin doesn't come off with this technique, it would probably be best to wait it out for the next shed.
I would also recommend using smaller perches. Large perches have been known to cause kinks in younger animals that do not usually show up until later in life. If given the choice, chondro usually prefer smaller perches over larger ones.
Other than the stuck shed, the chondro looks very healthy. Good luck and keep us posted as it grows. I have an 8 year old biak that is still changing color today.....they take their time.