We present GTC-OSIRIS phase-resolved optical spectroscopy of three compact binary millisecond pulsars, or 'spiders': PSR J1048+2339, PSR J1810+1744, and (for the first time) PSR J1908+2105. For the companion in each system, the temperature is traced throughout its orbit, and radial velocities are measured. The radial velocities are found to vary with the absorption features used when measuring them, resulting in different radial velocity curve semi-amplitudes: for J1048 ($K_\mathrm{metals, red} = 344 \pm 4{\mathrm{\, km\, s^{-1}}}{}$ and $K_\mathrm{metals, blue} = 372 \pm 3{\mathrm{\, km\, s^{-1}}}{}$) and, tentatively, for J1810 ($K_\mathrm{Balmer} = 448 \pm 19{\mathrm{\, km\, s^{-1}}}{}$ and $K_\mathrm{metals} = 491 \pm 32{\mathrm{\, km\, s^{-1}}}{}$). With existing inclination constraints, this gives the neutron star (NS) and companion masses $M_\mathrm{NS} = 1.50$-$2.04{\, {\rm M}_{\odot }}{}$ and $M_2 = 0.32$-$0.40{\, {\rm M}_{\odot }}{}$ for J1048, and $M_\mathrm{NS} \gt 1.7{\, {\rm M}_{\odot }}{}$ and $M_2 = 0.05$-$0.08{\, {\rm M}_{\odot }}{}$ for J1810. For J1908, we find an upper limit of $K_2 \lt 32{\mathrm{\, km\, s^{-1}}}{}$, which constrains its mass ratio $q = M_2 / M_\mathrm{NS} \gt 0.55$ and inclination $i \lt 6.0^\circ$, revealing the previously misunderstood system to be the highest mass ratio, lowest inclination redback yet. This raises questions for the origins of its substantial radio eclipses. Additionally, we find evidence of asymmetric heating in J1048 and J1810, and signs of metal enrichment in J1908. We also explore the impact of inclination on spectroscopic temperatures, and demonstrate that the temperature measured at quadrature ($\phi = 0.25\,\mathrm{ and}\,0.75$) is essentially independent of inclination, and thus can provide additional constraints on photometric modelling.