Personally I’ve found that too much fiber can only make things worse. I was severely constipated for two weeks and am only now starting to get things going. I’ve read that increasing the fat intake would be benefitial and have been now making sure that I eat fats with every meal instead of obsessing over getting enough fiber (as I used to). Seems to work.
One thing that has helped me in the past is drinking 2 Tbsp olive oil with half a lemon juice first thing in the morning. Then wait at least 20 minutes before eating anything. This is supposed to increase the bile production which then promotes bowel movements. I am not sure you should do this in the long term though; the doctor who recommended it only advised to use this for a week as part of a detox program.