Analyses of ground-based experiments on near-critical fluids to precisely determine their density can be hampered by several effects, especially the density stratification of the sample, the liquid wetting behavior at the cell walls, and a possible singular curvature of the "rectilinear" diameter of the density coexisting curve. For the latter effect, theoretical efforts have been made to understand the amplitude and shape of the critical hook of the density diameter, which depart from predictions from the so-called ideal lattice-gas model of the uniaxial 3D-Ising universality class. In order to optimize the observation of these subtle effects on the position and shape of the liquid-vapor meniscus in the particular case of SF6, we have designed and filled a cell that is highly symmetrized with respect to any median plane of the total fluid volume. In such a viewed quasi-perfect symmetrical fluid volume, the precise detection of the meniscus position and shape for different orientations of the cell with respect to the Earth's gravity acceleration field becomes a sensitive probe to estimate the cell mean density filling and to test the singular diameter effects. After integration of this cell in the ALI-R insert, we take benefit of the high optical and thermal performances of the DECLIC Engineering Model. Here we present the sensitive imaging method providing the precise ground-based SF6 benchmark data. From these data analysis it is found that the temperature dependence of the meniscus position does not reflect the expected critical hook in the rectilinear density diameter. Therefore the off-density criticality of the cell is accurately estimated, before near future experiments using the same ALI-R insert in the DECLIC facility already on-board the International Space Station.