It sounds to me as if you are doing everything right. Not everyone will experience constipation, particularly if they follow a few simple suggestions:

1) keep hydrated;
2) eat plenty of salt to keep your electrolytes in balance and water in your colon;
3) eat plenty of fat (this may be why ketogenic is working better for you than standard low carb)
4) eat most of your daily carbs as low starch vegetables
5) keep moving (walking at a comfortable pace for you is great exercise)

Keep up the good work!