Why do I keep seeing this equation for $E_b/N_0$
It's just a matter of finding out the assumptions behind the equation. Sometimes, unfortunately, those assumptions are not made explicit.
For the first equation you present, the one you have issues with, the assumptions are (off the top of my head):

Orthogonal, ideal sinc pulses are used as pulse shape.
The signals involved are strictly baseband, or, if passband, then the upconversion is suppressed-carrier, and the entire process is ideal.
The transmitted signal is narrowband; there are no multicarriers.
The channel is AWGN; there is no signal distortion, not even attenuation.
There is no coding and the transmitted bits are uncorrelated.
The received signal is matched-filtered. The matched filter is ideal (i.e. an infinite sinc pulse).

Under these assumptions, that equation is correct.
If you change those assumptions, then the relationship changes, as you found. I didn't check every one of you equations carefully but in general it seems like you are on the right track.