Ryan,
First off, I can't wait to see you guy's video, it looks good.
I have not had the same experience as you. I am currently shooting she same shaft with some Left helical, and some right helical arrows (I just got a new RW Clamp but I am still shooting my older LW Helical arrows) anyway, I have no POI shift between them. While I was tuning I turned my arrows little by little until I had no contact, again no shift in POI.
I wouldn't think that your POI shift would solely be on your feather position but would more likely be due to interference between your feather and the riser.
You can check this out by spraying your riser with aeresol foot powder and then shooting your arrows and looking for signs of feather impacting the riser, keep doing this until the foot powder is undisturbed. Hope this helps.
It could also be that as you are trying to gain the same anchor as you are rotating the feather around to different positions that you are slightly changing your form. This could also affect your POI.
BTW, I shoot 3 under, instinctive, cock feather in also.