Solving large-scale instances of the multiple traveling repairman problem with profits (MTRPP) poses a significant computational challenge with direct implications for logistics and emergency response. To address this challenge, this work introduces a multi-start hyper-heuristic with a greedy selection mechanism (MSHGSM), an approach specifically developed to solve large and complex MTRPP instances. The approach leverages a multi-start framework to ensure robust coverage of the solution space and a greedy selection mechanism to iteratively apply the most effective move from a pool of twelve low-level heuristics. This process is guided by an adaptive perturbation technique that strategically manages the trade-off between exploiting known solutions and exploring new possibilities. The performance of MSHGSM is validated through extensive experiments on established benchmarks, where it proves significantly superior to existing methods on large instances. MSHGSM not only improves the best-known solutions for 22 out of 30 large instances, but it also exhibits competitive computational efficiency. While other algorithms may be better suited for medium-sized problems, MSHGSM is demonstrably the most effective for solving large, complex MTRPP instances.