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The optical floating zone crystal growth technique is a well-established method for obtaining large, high-purity single crystals. While the floating zone method has been constantly evolving for over six decades, the development of high-pressure (up to 1000 bar) growth systems has only recently been realized via the combination of laser-based heating sources with an all-metal chamber. While our inaugural high-pressure laser floating zone furnace design demonstrated the successful growth of new volatile and metastable phases, the furnace design faces several limitations with imaging quality, heating profile control, and chamber cooling power. Here, we present a second-generation design of the high-pressure laser floating zone furnace, "Laser Optical Kristallmacher II" (LOKII), and demonstrate that this redesign facilitates new advances in crystal growth by highlighting several exemplar materials: α-Fe2O3, β-Ga2O3, and La2CuO4+δ. Notably, for La2CuO4+δ, we demonstrate the feasibility and long-term stability of traveling solvent floating zone growth under a record pressure of 700 bar. [ABSTRACT FROM AUTHOR]