Why haven't I come across any references to the DF in literature on GG? Given that the main goal of the approach lies in detecting the properties Language exhibit, what role do such long known traits as Double Articulation play in this? Moreover, I have heard Chomsky claimed that investigating other semiotic systems than natural languages gives nothing to the task. Why? May they be implicitly assumed? By far, there must exist some principles which would make it possible to differenciate between the entities operating in the derivation.
I am reasonably sure that Chomsky would not agree with you that "the main goal" is to collect properties of Language. The goal is to understand human language.
Non-human animals have semiotic systems, but Chomsky's position is that the important characteristics of human language are species specific to humans.