Reconstruction of highly accurate CAD models from point clouds is both paramount and challenging in industries such as aviation. Due to the acquisition process, this kind of data can be scattered and affected by noise, yet the reconstructed geometric models are required to be compact and smooth, while simultaneously capturing key geometric features of the engine parts. In this paper, we present an iterative moving parameterization approach, which consists of alternating steps of surface fitting, parameter correction, and adaptive refinement using truncated hierarchical B-splines (THB-splines). We revisit two existing surface fitting methods, a global least squares approximation and a hierarchical quasi-interpolation scheme, both based on THB-splines. At each step of the adaptive loop, we update the parameter locations by solving a non-linear optimization problem to infer footpoints of the point cloud on the current fitted surface. We compare the behavior of different optimization settings for the critical task of distance minimization, by also relating the effectiveness of the correction step to the quality of the initial parameterization. In addition, we apply the proposed approach in the reconstruction of aircraft engine components from scanned point data. It turns out that the use of moving parameterization instead of fixed parameter values, when suitably combined with the adaptive spline loop, can significantly improve the resulting surfaces, thus outperforming state-of-the-art hierarchical spline model reconstruction schemes.