Context. As evidenced by recent survey results, the majority of asteroids are slow rotators (spin periods longer than 12 h), but lack spin and shape models because of selection bias. This bias is skewing our overall understanding of the spins, shapes, and sizes of asteroids, as well as of their other properties. Also, diameter determinations for large (>60 km) and medium-sized asteroids (between 30 and 60 km) often vary by over 30% for multiple reasons. Aims. Our long-term project is focused on a few tens of slow rotators with periods of up to 60 h. We aim to obtain their full light curves and reconstruct their spins and shapes. We also precisely scale the models, typically with an accuracy of a few percent. Methods. We used wide sets of dense light curves for spin and shape reconstructions via light-curve inversion. Precisely scaling them with thermal data was not possible here because of poor infrared datasets: large bodies tend to saturate in WISE mission detectors. Therefore, we recently also launched a special campaign among stellar occultation observers, both in order to scale these models and to verify the shape solutions, often allowing us to break the mirror pole ambiguity. Results. The presented scheme resulted in shape models for 16 slow rotators, most of them for the first time. Fitting them to chords from stellar occultation timings resolved previous inconsistencies in size determinations. For around half of the targets, this fitting also allowed us to identify a clearly preferred pole solution from the pair of two mirror pole solutions, thus removing the ambiguity inherent to light-curve inversion. We also address the influence of the uncertainty of the shape models on the derived diameters. Conclusions. Overall, our project has already provided reliable models for around 50 slow rotators. Such well-determined and scaled asteroid shapes will, for example, constitute a solid basis for precise density determinations when coupled with mass information. Spin and shape models in general continue to fill the gaps caused by various biases.