If I understood correctly it would be really difficult to solve for the changing Cl on the based when the control surfaces deflect since there are too many variables. Probably, a "close enough" estimation can be made by putting a piece of my wing in a wind tunnel and record how the Cl changes as the control surface deflects. However, it would not be 100% since all the variables would not be present when testing.

Do you know any literature that I can read that talks more about the deflection of the control surfaces?

Thank you again.