I don’t know if either the Master cleanse or the juice fast will cure your constipation problem.
My suggestion is the following: go on a 5 day juice fast - don’t be too strict with yourself. Take daily cleansing enemas followed by a retention coffee enema during the fast. Follow the fast with a change of diet, more veggies, less or no red meats. Eat fish and fowl. Don’t take vitamins and supplements during the first 3 days of the fast but take them after that.
You can take more fiber not psyllium but use freshly ground flax seed every morning for a week or two. Then stop for awhile. Start again if you are still constipated. Repeat this process for several months or until your constipation is cured. I believe that a predisposition to constipation can be inherited and if that is the case it is very difficult to cure it. My father suffered from it and my mother had it so bad that after she started menopause she could not have a bowel movement without a laxative or an enema. This kept on until her passing on. I suffered from it until I changed my life style completely. Change of diet, exercise and avoid stressful situations.
Please read my blog titled “My challenge”, link below. Don’t hesitate to ask questions. I hope this gives you some hope.