Bertonneau would probably be sympathetic but not particularly interested. He blogs on the Orthosphere, a fairly well known reactionary site, but is much more of traditionalist than I am. He's been connected to GA almost from the beginning, much longer than I've been--he was a very early student of Gans's--and is of course thoroughly "fluent" in it (and has written some excellent introductions, scattered across the internet), but uses it more for interpretative than, let's say, "reconstructive" purposes. He's actually also very interested in the cognitive implications of literacy, but here, as well, mostly to analyze the degeneracy of contemporary modes of consciousness. He's very worth reading, but he's got his own projects. To put it another way, he "uses" GA insofar as it converges with interests he has independent of it; I'm interested in GA as a total discipline.
Ultimately these would be questions for Bertonneau. The "cognitive implications of literacy" he focuses on are the ability to construct linear, rational discourse--e.g., to distinguish between conjecture and factual claims. In this context, he argues that these cognitive "acquisitions" of literacy are being systematically undermined by contemporary liberalism (consumerism, communications technology, victim mongering, etc.). He often uses his students as examples of these developments. I'm not sure how he thinks about the reconstruction of tradition--he seems to me more focused on the intellectual and moral resistance to long terms degenerative developments like gnosticism.
I don't think so much in terms of "gnosticism" anymore, but gnosticism believes it possesses the truth about the world to which everyone else is blinded--to put it bluntly, what everyone else thinks is God is really the Devil. I think this should be approached differently--everyone has the truth, because everyone has language, and it's therefore a question of showing how the origin of language is implicit in all utterances. The further implication would be that all traditions have been approaching an understanding of the originary hypothesis--they have all been what Oulipo calls "anticipatory plagiarists," but we need to show how. The originary hypothesis is both the most astonishing discovery and the merest tweak on what everyone has always known.