After 20+ hours of going through the full street game, I can assure you that the above assumptions are total bunk. I still have a lot of confusion. The core of which is that it's hard to establish a range when there are multiple streets of betting. There is not clear cut division of starting range that I have proved is correct. I can only assume different split points and show that one is better than another.

This is something that I can't get off my mind... It's so simple, but so complex.

FWIW, with the full street [0, 1] game, Villain only b/c's with the top 2 best hands, and b/f's only the 1 hand dictated by the call value in the half-street game. This value is the line between c/c and c/f. This minimizes Hero's EV. I found this by trial and error, not proof. I don't know how many divisions in Villain's range are appropriate. The above is based on assuming villains range is something like:
|--b/c--|--c/c--|--b/f--|--c/f--|
right now