This paper presents further improvements to the immersed boundary method introduced in [1]. The proposed developments take place during the pre- and post-processing stages of the simulation workflow and aim to further increase the accuracy of the approach for steady-state simulations of high Reynolds number turbulent flows around aerodynamic geometries facing strong incidence. To this end, the location of the forcing points is further optimized prior to simulation, with an adaptive and local modeling height that accounts for the evolution of the turbulent boundary layer thickness, especially at the leading edge. In addition, the direct extrapolation of the pressure solution at the wall is replaced by first- and second-order reconstructions using the normal pressure gradients interpolated at a new set of image points. This second approach is used only in post-processing, after the simulation, and prevents the degradation of the wall pressure in the presence of strong curvatures or thin boundary layers. These developments have been validated by simulating subsonic turbulent flows around the NACA0012 profile, 2D multi-element airfoil (2DMEA), and HL-CRM half-plane at significant angles of attack. Smooth and accurate skin pressure and friction coefficients are observed, in excellent agreement with body fitted wall-resolved solutions, even for coarser Cartesian meshes. Better drag and lift coefficients calculated by direct near-field integrations are obtained, along with accurate predictions of the near-wall flow physics throughout the turbulent boundary layer.