Fronting for
who? Surely, you don't mean the Zhodani dummy corporation, which only showed up on Fulacin around 1099,
over 700 years after the Octagon Society ceased functioning as an interstellar organization.*
They certainly weren't there during the Third Frontier War (979 - 986) either, or else that intolerably soporific poet would have jotted something down about it before he died.
There is absolutely no evidence, anywhere, that the Octagon Society of the 300-400s was anything other than what it said it was on the tin. With the exception of a very basic, octagon shaped space station on Risek, all they were ever reported to do was go around building rustic wilderness retreats, the far-future equivalent of a
bothy, none of which would have any serious strategic or military value.
*There is still one active chapter of the organization on Wochiers, due to the uniquely challenging environment of that world, but it is solely involved local affairs, other than the occasional archival service.