I hope you followed along with all of that. But here's the catch:
As far as I know, the RED ONE does not have anything in it's optical system that is affected by the polarization of light. There isn't a semi-polarized mirror in between the exit pupil of the lens and the sensor. A high-pass/infrared filter in front of the sensor won't be affected by polarized light.
Why spend more on the circular polarizer? Probably because the safe bet has seemed to be splurging on the circular just in case. I also find it common for people to believe that "circular" means it's the only one you can rotate to vary the effect. Misinformation, uncertainty, and doubt.
Put it all to rest now. If you're looking to buy a polarizer, get a linear if it'll save you money. In fact, why not, try and find a clean, scratch-free used one?
Granted, I don't own a RED ONE. So if anyone out there wants to actually test it in the real world, please do, and post your results here.
Great post! I was planning to get a linear pola for these same reasons, but I ended up going with circular because of the auto-focus and optical viewing systems that are coming out.