It is definitely possible to cut in the intermediate stage, but try to make it a gradual cut. Make it a long term goal and aim for .5-1lbs (.25/.5kg) per week over a few month period. Weigh yourself on a bathroom scales first thing in the morning, if your weight goes down a pound you ate -3,500kcal (-500/day) below maintenance. Vice-versa if you gain weight. Over a 6 month period you could lose 12-24lbs this way.
I was at 27% bf about a month ago when I started SS, but have used an approach to try not to gain any weight as a measure of LBM increasing. I am probably getting closer to 20%, lost a few inches around the waist.
Also, opinions differ on this but a lot of calisthenics pros advise against doing pull-ups to failure. It may be an evolutionary throwback to a time when we were swinging in trees and failure meant falling to your death, but the body has a strange response to failure on pull-ups and the muscles don't adapt as quickly as they would if you left 1 or 2 in the tank.