But Cl(max) remains the same regardless of CG position - that's the point. Similarly the stalling angle-of-attack (alpha) also remains the same regardless of CG position. The speed at which the stalling angle is achieved in S&L flight will increase slightly as static margin increases (for a tailplane-at-the-back aeroplane), but this is not because Cl(max) has changed because it doesn't.
But for calculation purposes it can be useful to model it as a Cl(max) shift as a convenient conceit, in the same way that when analysing material properties it is a convenient conceit to assume that atoms solid, uniform spheres packed so close together that they touch their neighbours in a lattice, or when analysing cyclic motions it can be convenient to assume that -1 has a square root and it governs the behaviour. None of these are literally true - they are just convenient way of looking at or modelling things in specific contexts.
[soap-box mode]
As for stalling speeds in flight manuals - this is something I have always argued against because they are dangerously misleading. Stall speeds vary with weight, bank angle, CG, air density, phase of the moon and ambient mean grandmother's age (I may have made some of those up).
I have ALWAYS felt that all aircraft should simply be equipped with a good alpha gauge, because stalling alpha only really varies with density altitude (and even then not dramatically) so it would be extremely simple to have a single instrument which tells you directly and accurately just how close you are to stalling - it could even incorporate air density correction (mechanically - no bug-prone safety-critical software needed). Fast jet pilots love 'em, they're no more expensive to make than (say) a decent turn & slip indicator, and there's no earthly reason why this wonderful safety-enhancing instrument couldn't be a mandatory inclusion in everything from VLA upwards.
[end of soapbox mode]