Today, versatile emission computed tomography (VECTor) technology using dedicated high-energy collimation enables simultaneous positron emission tomography (PET) and single photon emission computed tomography (SPECT) down to 0.6 mm and 0.4 mm resolution in mice, respectively. We recently showed that for optimal resolution and quantitative accuracy of PET images the long tails of the 511 keV point spread functions (PSFs) need to be fully modelled during image reconstruction. This, however, leads to very time consuming reconstructions and thus significant acceleration in reconstruction speed is highly desirable. To this end we propose and validate a combined dual-matrix dual-voxel (DM-DV) approach: for the forward projection the slowly varying PSF tails are modelled on a three times rougher voxel grid than the central parts of the PSFs, while in the backprojection only parts of the PSF tails are included. DM-DV reconstruction is implemented in pixel-based ordered subsets expectation maximization (POSEM) and in a recently proposed accelerated pixel-based similarity-regulated ordered subsets expectation maximization (SROSEM). Both a visual assessment and a quantitative contrast-noise analysis confirm that images of a hot-rod phantom are practically identical when reconstructed with standard POSEM, DM-DV-POSEM or DM-DV-SROSEM. However, compared to POSEM, DM-DV-POSEM can reach the same contrast 5.0 times faster, while with DM-DV-SROSEM this acceleration factor increases to 11.5. Furthermore, mouse cardiac and bone images reconstructed with DM-DV-SROSEM are visually almost indistinguishable from POSEM reconstructed images but typically need an order of magnitude less reconstruction time.