We demonstrate a new approach for climate model tuning in a realistic situation. Our approach, described in detail in Part I, systematically uses a single-column configuration of a global atmospheric model on a series of test cases for which reference large-eddy-simulations are available. The space of free parameters is sampled running the single-column model from which metrics are estimated in the full parameter space using emulators. The parameter space is then reduced by retaining only the values that are consistent with the metrics computed on large eddy simulations within a given tolerance to error. The approach is applied to the recently designed 6A version of the LMDZ model, itself the result of a long investment in the development of physics parameterizations and by-hand tuning. The boundary layer is revisited by increasing the vertical resolution and varying parameters that were kept fixed so far. The approach allows us to automatically reach a tuning as good as that of the 6A version, after some improvements are done at process scale. This approach helps accelerate the introduction of new parameterizations, by avoiding a tedious manual tuning process and preventing some of the error compensations that could occur if calibration was carried out directly with the full atmospheric model. This way of using machine learning techniques allows us to maintain the physical foundations of the model and to ensure that the improvement of global metrics is obtained for a reasonable behavior at process level. That is, we get things right for the right reasons.