The roots of constipation start higher up the pipe. Have you tried strengthening your digestion in the stomach by taking digestive enzymes with your meals? If your stomach is not secreting enough HCL to digest your food, you will have problems further down the pipe. HCL secretion is a parasympathetic response, which means you need to be reasonable relaxed at mealtimes for your stomach to work properly. If your liver and gallbladder are highly congested, in addition to not having enough HCL you may not be releasing enough bile and what little bile you are producing may be getting bound up in the fiber supplement.
If you prefer digestive enzymes to ayurvedic herbs, I'd recommend taking a product that has betaine HCL along with taurine and pancreatic enzymes to help boost the digestion. Betaine is made from beets and helps to thin the bile to get it moving.