The Mott-insulating rare-earth titanates ($R{\mathrm{TiO}}_{3}$, with $R$ being a rare-earth ion) are an important class of materials that encompasses interesting spin-orbital phases as well as ferromagnet-antiferromagnet and insulator-metal transitions. The growth of these materials has been plagued by difficulties related to overoxidation, which arises from a strong tendency of ${\mathrm{Ti}}^{3+}$ to oxidize to ${\mathrm{Ti}}^{4+}$. We describe our efforts to grow sizable single crystals of ${\mathrm{YTiO}}_{3}, {\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{TiO}}_{3}$ ($x\ensuremath{\le}0.25$), and ${\mathrm{Y}}_{1\ensuremath{-}y}{\mathrm{Ca}}_{y}{\mathrm{TiO}}_{3}$ ($y\ensuremath{\le}0.35$) with the optical traveling-solvent floating-zone technique. We present sample characterization via chemical composition analysis, magnetometry, charge transport, neutron scattering, x-ray absorption spectroscopy, and x-ray magnetic circular dichroism to understand macroscopic physical property variations associated with overoxidation. Furthermore, we demonstrate a good signal-to-noise ratio in inelastic magnetic neutron scattering measurements of spin-wave excitations. A superconducting impurity phase, found to appear in Ca-doped samples at high doping levels, is identified as TiO.