avoid fiber or the cleanse diet/kit until you are properly hydrated
a lot of times if you eat fiber without the proper amount of water to flush it through the fiber will have to absorb moisture from your body to be digested and will and further your constipation...unless, like goodsamaritain said, its in the form of hydrating fruit, the best is watermellons as they will add a generous amount of fluid and a lower sugar content per cup then any other fruit, also good are cucumbers, and celery(chew it up and spit out the fiber, its a great source of natural minerals)
if you want to do an apple fast make sure its the whole apple(and a lot of water, a little
mineral salt and possibly oil since you do not have a good source of animal fat )not just the juice...the whole apple will be less detrimental to your blood sugar, keeping it more even, also the pectin in the skins is said to aid digestion...
i would suggest less meals per day as well, so your body is not constantly digesting....i have a feeling if you are eating this many meals you are mistaking thirst for hunger! i often feel "hungry" 1.5-2hrs after my meal of the day, i make hot water and drink a few cups and feel better and also like it aids digestion
also be sure to check the cleanse to make sure it does not contain pysillium or another type of fiber or something like magnesium or senna, these will all dehydrate you further so you will have to be very aware of the need for extra water with mineral content so your electrolytes do not go out of balance, which can cause water retention in addition to constipation
cheese is constipating to almost everyone i know, unless they have intolerance, then it is explosive!
jogging/jumping jacks can help tone the bowels by stimulating them with movement. as well as stretching, there are great yoga posses that will help push turds around, you can find these on the internet.
hydrate!!! hope any of this helps