This paper proposes a complete algorithm stack for large-scale multi-robot assembly planning. In leveraging mobile autonomous robots to innovate manufacturing processes, we focus on addressing challenges such as collision-free movement in shared workspaces, effective multi-robot collaboration for handling and transporting large payloads, complex task allocation due to complex manufacturing processes, and space planning for parallel assembly and transport of nested subassemblies. Given CAD-like product specifications as input, we propose an algorithm stack that automatically plans the complete assembly sequence of a robot group to manufacture the product. This stack consists of: ① an iterative radial layout optimization procedure for defining the global staging layout of the manufacturing facility; ② a graph-recovery mixed-integer programming formulation and a modified greedy task assignment algorithm for optimally assigning robots and robot subteams to assembly and transport tasks; ③ a geometric heuristic and hill-climbing algorithm for planning collaborative transport configurations for robot subteams; and ④ a distributed control policy that ensures collision-free execution of the assembly motion plans. Furthermore, we provide an open-source multi-robot manufacturing simulator implemented in Julia as a resource for testing the algorithm and furthering multi-robot manufacturing research. Experimental results demonstrate the scalability and effectiveness of the approach by generating the manufacturing plan for the LEGO model of the Saturn V launch vehicle, consisting of 1,845 parts, 306 subassemblies, and 250 robots, in less than three minutes on a standard laptop computer.