What you have been missing here is one simple thing- Lift=Weight in level, unaccelerated flight. As such there is no one value for Cl in a particular configuration.
If you consider that L=M, and L= Cl*1/2Rho*V^2*A (Where A is wing area), plug ther variables in for a particular weight and speed, you get a value for Cl. Change any value, and you change Cl.