We present the first free-floating autonomous underwater construction system capable of using active ballasting to transport cement building blocks efficiently. It is the first free-floating autonomous construction robot to use a paired set of resources: compressed air for buoyancy and a battery for thrusters. In construction trials, our system built structures of up to 12 components and weighing up to 100Kg (75Kg in water). Our system achieves this performance by combining a novel one-degree-of-freedom manipulator, a novel two-component cement block construction system that corrects errors in placement, and a simple active ballasting system combined with compliant placement and grasp behaviors. The passive error correcting components of the system minimize the required complexity in sensing and control. We also explore the problem of buoyancy allocation for building structures at scale by defining a convex program which allocates buoyancy to minimize the predicted energy cost for transporting blocks.