Multi-robot systems have shown increasing viability in construction due to their ability to execute high-precision actions while reducing human exposure to hazardous tasks. However, these environments have high-dimensional configuration spaces and possess substantial collision-avoidance constraints, which include other robots, assembly objects, and workspace boundaries. We utilize a single factor graph for trajectory estimation and planning that incorporates measured robot states together with explicit collision and learned cable constraints. This supports changing workspaces and enables synchronized, high-dimensional robot motion planning while accounting for the stiff, vibration-induced uncertainty of heavy robotic systems. We demonstrate the success of our framework on the construction of a post-and-lintel structure using one robot arm as a timber gripper, and a second robot as a nail-fastener.