Adapting graham cracker crust to all-natural graham crackers
I have used Midel brand ginger snaps, graham crackers, and lemon snaps in crust recipes and they all happen to perform well in standard recipes. They do in fact have a better taste with respect to the snaps; the graham crackers I didn't notice much return on investment. The wholesome ingredients are not detrimental to their ability to be pressed into a shell. 

I would recommend trying the recipe as-is first with the Midel cookies. My guess is that you are concerned that they will be too dry or something to that effect, or would crumble rather than bind together. For a shell like this I would be sure to parbake and grease the pan with shortening rather than any kind of spray. When you remove the crust, if it seems drier than usual, I would brush a minor amount of canola oil over top.

If you want to improve on this with respect to things you can likely buy at a natural food market, I would begin by greasing the pan with coconut oil and brushing with walnut or almond oil oil. This will also add $3 to the cost of your crust.

In general, Midel bakes well as far as my experience has gone.