X-ray grating interferometry is a coherent imaging technique that bears tremendous potential for three-dimensional tomographic imaging of soft biological tissue and other specimens whose details exhibit very weak absorption contrast. It is intrinsically trimodal, delivering phase contrast, absorption contrast, and scattering ("dark-field") contrast. Recently reported acquisition strategies for grating-interferometric phase tomography constitute a major improvement of dose efficiency and speed. In particular, some of these techniques eliminate the need for scanning of one of the gratings ("phase stepping"). This advantage, however, comes at the cost of other limitations. These can be a loss in spatial resolution, or the inability to fully separate the three imaging modalities. In the present paper we report a data acquisition and processing method that optimizes dose efficiency but does not share the main limitations of other recently reported methods. Although our method still relies on phase stepping, it effectively uses only down to a single detector frame per projection angle and yields images corresponding to all three contrast modalities. In particular, this means that dark-field imaging remains accessible. The method is also compliant with data acquisition over an angular range of only 180° and with a continuous rotation of the specimen.