Driven by the increasing number of marine data science applications, there is a growing interest in surveying and exploring the vast, uncharted terrain of the deep sea with robotic platforms. Despite impressive results achieved by many on-land visual mapping algorithms in the past decades, transferring these methods from land to the deep sea remains a challenge due to harsh environmental conditions. Typically, deep-sea exploration involves the use of autonomous underwater vehicles (AUVs) equipped with high-resolution cameras and artificial illumination systems. However, images obtained in this manner often suffer from heterogeneous illumination and quality degradation due to attenuation and scattering, on top of refraction of light rays. All of this together often lets on-land SLAM approaches fail underwater or makes Structure-from-Motion approaches drift or omit difficult images, resulting in gaps, jumps or weakly registered areas. In this work, we present a system that incorporates recent developments in underwater imaging and visual mapping to facilitate automated robotic 3D reconstruction of hectares of seafloor. Our approach is efficient in that it detects and reconsiders difficult, weakly registered areas, to avoid omitting images and to make better use of limited dive time; on the other hand it is computationally efficient; leveraging a hybrid approach combining benefits from SLAM and Structure-from-Motion that runs much faster than incremental reconstructions while achieving at least on-par performance. The proposed system has been extensively tested and evaluated during several research cruises, demonstrating its robustness and practicality in real-world conditions.