A recap for Lurkers on the definition project: we are agreed to the following definition of an intelligent design hypothesis subject to an agreement on a definition for intelligence:
Intelligence - decision-making, awareness and purpose whether fractal, emergent or otherwise.
Conversely, the word experiential would limit intelligence by experience (i.e. embodiment) which would stand in favor of fractal and against emergent intelligence.
Either adjective could also redirect this project into a discussion of the false "Cartesian split" which I don't believe we wish to do at this time.
Also, the phrase reasoned purpose doesnt get the point of intentionality across, as you say, and IMHO doesnt give enough weight to property of decision-making or reasoning.
My counter-proposal:
Intelligence - comprehension, awareness, intentionality, and reasoning whether fractal, emergent, or otherwise.
That attributes the intention and reason to the entity under consideration.
That also gives each of eight different complex terms one of eight different suffixes. A form of linguistic beauty that warms my heart. =)