RE: Wing chord and Alpha limit
Yeah, it seemed like sort of a funny reason to dump the system. But engineers need to be able to describe their stuff mathematically and that infinity issue is not something that makes for clean math. By switching to a convention that puts the lift center at the 25% chord point and then just deals with the "torque" by describing it as a pitching moment at worst the value will go to 0. And that's something that works out a lot better for calculations of any sort.
Either system works. After all it's just a way of describing how the wing is producing it's lift. The convention for describing it that works best with the other aspects that need to be considered is obviously going to be the cleanest one.
Where are the guys like Ben Lanterman and Bank2Turn when you need their input? They worked in aerodynamics engineering and could better explain some of the reasons for the shift. I'm pretty much parroting what they have said in the past about this but I may be getting some of it wrong.
Cola, I think you may not have some of your Cp locations quite right. It's been a while but I seem to remember that the Center of Pressure tended to move forward with increasing angle of attack until at the stall it was at the leading edge or perhaps it was said to "fall off the front" of the leading edge at the stall point or such thing. I may be mis-remembering this aspect. I never really looked at all this stuff seriously until the fixed life locus and pitching moment was being used and that's the one I learned to understand.
Why is the pitching moment idea better? Because since the pitching moment is a torque it is easier to look at a torque from the wing and a torque (lift) from the horizontal tail and understand that the stabilizer will be able to deal with the wing's behaviour or not.