Terahertz (THz) external-cavity lasers based on quantum-cascade (QC) metasurfaces are emerging as widely-tunable, single-mode sources with the potential to cover the 1-6 THz range in discrete bands with milliwatt-level output power. By operating on an ultra-short cavity with a length on the order of the wavelength, the QC vertical-external-cavity surface-emitting-laser (VECSEL) architecture enables continuous, broadband tuning while producing high quality beam patterns and scalable power output. The methods and challenges for designing the metasurface at different frequencies are discussed. As the QC-VECSEL is scaled below 2 THz, the primary challenges are reduced gain from the QC active region, increased metasurface quality factor and its effect on tunable bandwidth, and larger power consumption due to a correspondingly scaled metasurface area. At frequencies above 4.5 THz, challenges arise from a reduced metasurface quality factor and the excess absorption that occurs from proximity to the Reststrahlen band. The results of four different devices -with center frequencies 1.8 THz, 2.8 THz, 3.5 THz, and 4.5 THzare reported. Each device demonstrated at least 200 GHz of continuous single-mode tuning, with the largest being 650 GHz around 3.5 THz. The limitations of the tuning range are well modeled by a Fabry-Pérot cavity which accounts for the reflection phase of the metasurface and the effect of the metasurface quality factor on laser threshold. Lastly, the effect of different output couplers on device performance is studied, demonstrating a significant trade-off between the slope efficiency and tuning bandwidth.