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The elastic surface algorithm (ESA) is an iterative inverse design method for airfoils, considering the airfoil wall as an elastic curved beam pinned at its beginning and ending points. This structure deforms in response to the disparity between existing and target pressure distributions. This paper introduces an improvement to the ESA, allowing controlled movement of the airfoil's leading edge within a vertical groove. This advancement enables the adjustment of the angle of attack during the inverse design process, enhancing the airfoil's robustness and flexibility. In contrast to a fixed angle of attack approach, the proposed method prevents unrealistic geometric features, such as airfoil fishtailing, improving convergence potential. The developed method was validated through the inverse design of NACA0012 and FX63-137 airfoils in a viscous subsonic flow regime. The flow solver was validated using existing experimental results, showing good agreement. Finally, the pressure distribution of the FX63-137 airfoil was modified to increase lift or decrease drag. The corresponding geometries were obtained via the advanced ESA method, resulting in an almost 4 % increase in the lift-to-drag ratio. [ABSTRACT FROM AUTHOR]