Dissipative nonlinear wave dynamics have been investigated extensively in mode-locked lasers with single transverse-mode, whereas there are few studies related to three-dimensional nonlinear dynamics within lasers. Until recently, multi-transverse-mode, or spatiotemporal, mode-locking (STML) was demonstrated in lasers with small modal (i.e., transverse-mode) dispersion, which is critical for achieving STML because the small dispersion can be easily balanced. Here, we demonstrate that STML can be achieved in lasers with much larger modal dispersion, and we find that the spatiotemporal self-organization of the multimode solitons is quite different from previous studies. Furthermore, we observe a new STML phenomenon of passive nonlinear auto-selection of single-mode mode-locking, resulting from the interaction between spatiotemporal saturable absorption and spatial gain competition. Our work significantly broadens the design possibilities for useful STML lasers thus making them much more accessible for applications, and extends the explorable parameter space of the novel dissipative spatiotemporal nonlinear dynamics that can be achieved in these lasers.