Three-dimensional fluorescence microscopy is a key technology for inspecting biological samples, ranging from single cells to entire organisms. We recently proposed a novel approach called spatially modulated Selective Volume Illumination Microscopy (smSVIM) to suppress illumination artifacts and to reduce the required number of measurements using an LED source. Here, we discuss a new strategy based on smSVIM for imaging large transparent specimens or voluminous chemically cleared tissues. The strategy permits steady mounting of the sample, achieving uniform resolution over a large field of view thanks to the synchronized motion of the illumination lens and the camera rolling shutter. Aided by a tailored deconvolution method for image reconstruction, we demonstrate significant improvement of the resolution at different magnification using samples of varying sizes and spatial features.