Grating-coupled, surface-emitting (GCSE) quantum-cascade lasers (QCLs) offer a pathway towards realizing watt-range, surface-emitted output powers in the mid-infrared spectral region with high beam quality. Previously we have reported wide-ridge GCSE QCLs which employed metal/semiconductor, 2nd-order distributed feedback (DFB) gratings with distributed Bragg reflector (DBR) terminations. We report here on the lasing characteristics of narrow-ridge (similar to 7 mu m-wide) GCSE devices, which employ the STA-RE-type active-region design, for obtaining single-spatial-mode both laterally and longitudinally. The QCL structure was grown using Metalorganic Chemical Vapor Deposition (MOCVD) and the grating was defined using a combination of e-beam lithography patterning and wet-chemical etching, and the ridge (similar to 7 mu m) was dry-etched. The total length of the DFB + DBR regions is 5.1 mm, and was electrically isolated in the DBR regions by employing AlOx. Due to resonant coupling of the guided light to the antisymmetric surface-plasmon modes of the 2nd-order grating, the antisymmetric (A) modes are strongly absorbed; thus, allowing for the symmetric (S) mode to be favored to lase. Initial devices have demonstrated maximum pulse output power from the surface of similar to 150 mW at 4.88 mu m, with only similar to 10% power emitted from the edge facets. An anti-reflective (AR) coating of a quarter-wavelength Y2O3 layer was applied on the emission window, drastically improving the far-field beam pattern, that resulting in a central, near-diffraction-limited single-lobe beam pattern. COMSOL simulations were performed to further optimize the SE-base design for high CW performance. Parameter sweeps of cladding-layer thickness, grating height, and grating duty cycle were performed, which identified design tradeoffs for the various structural parameters.