I wouldn't presume to set you straight, stilzkin, but I will try to state my case on the subject.
I can't speak for the pronunciation of Atsayunk by the Atsiyonks. To me it seems difficult to find a path from Atsayunk to At-see-on, but I'm neither a linguist nor an expert on the Lenape or their language.
That being said, I can testify that in my sixty-five years as a lifelong resident of Shamong and Tabernacle, I have never heard anyone who has lived their life in the area pronounce Atsion as At-see-on. Generations of my family from my great-great-grandfather to my brother and his children have lived on Atsion Road. My great-great uncle was interviewed by Henry Charlton Beck for the chapter on Atsion in "Forgotten Towns of Southern New Jersey." I can't speak for the first two generations, but I don't believe that my grandfather took up the long I in Atsion as a symbol of youthful rebellion. I think he said it the way his elders and locals did, with the long I.
In my experience, At-see-on is said by visitors and folks who have moved into the area. The fact that it is now heard locally more frequently than in the past is understandable (though IMO unfortunate) given the dilution of long-time residents by more recent arrivals. Boyd, I don't doubt that you had neighbors who used the At-see-on pronunciation. However I do doubt that those who did had deep roots in the area.
In a totally unscientific recent survey by yours truly of YouTube videos about Atsion (excluding videos where the word Atsion is not said, such as drone videos), for the top twelve returns, only three used the long I, two used At-shun (At + generic pronunciation of -sion, which somehow doesn't seem quite as bad as At-see-on), and the other seven used At-see-on. I will note that out of these twelve, only one featured someone possessing historical & cultural bona fides, Barbara Solem. She used the long I for Atsion. I would trust the pronunciation used by her and the two local park agents over that of a reporter from Union County.
Considering all of the critical issues the world faces, and for that matter all of the critical issues the Pine Barrens face, this is a petty issue. Given that, though, Atsion is a very meaningful place name in my life, part of my heritage, including its traditional pronunciation. To me, the At-see-on pronunciation is an analog to an invasive species that could one day choke out the old-time long I version. (My brother fathered ten children, so perhaps in the process he may also have preserved the long I for at least one more generation. None of my nieces and nephews would ever say At-see-on.)
So with tongue in cheek, I will close by saying that I'll give up the long I in Atsion when someone pries it from my cold dead voice box.
(Note: I'm not differentiating between those who say Atsion in two syllables as At-sign and those who stretch -sign into two syllables, At-si-on. Both use the long I second syllable, which to me seems the most important feature. Both sound similar to each other, and dissimilar to At-see-on.)
Or is it 
