You poor thing, my mother had eczema for ages and it tortured her. I don't know about the effects a Water Fast has on eczema but one thing you said concerned me a little. You said that you are planning to walk for 3 to 4 hours a day...that is a lot of walking! This is concerning for 2 reasons; a Water Fast provokes a huge detoxification of the body and hence the body needs a lot of rest to recover. I am all for going for a walk to clear your mind and give your body some exercise but your goal seems very excessive. This brings me to the second reason why it concerns me; you mentioned that you have tried to fast many times and unfortunately failed. Maybe if you set a more palatable amount of walking, you would find it easier to do.
Let me be clear, fasting is a wonderful and enriching, not to mention healing experience, but it is very taxing on your body and your mind if you do not rest and refrain from excessive exercise.