To realize laser-driven high-luminance white light sources, many reflective configurations have been studied, often resulting in a challenging optical design. In this paper it is demonstrated that the efficacy of a transmissive configuration can be significantly enhanced by using a sapphire half-ball lens as out-coupling optic. This lens not only improves efficiency, but also drastically increases the potential light output due to improved heat dissipation from the single-crystal phosphor converter. Both claims are substantiated with detailed experimental results and realistic opto-thermal simulations, showing a light output of 6550 lm and over 20000 lm, respectively and corresponding luminance of 67 MCd/m2 and 209 MCd/m2.