We consider strongly confined, stably stratified shear flows generated as a lock exchange in a tube inclined at an angle of θ=45(∘). This paper focuses on a transitional regime, in which the flow alternates between two distinct states: laminar, parallel shear flow and intense transverse motion characteristic of turbulence. Laminar-turbulent cycles were captured at Atwood numbers At≡(ρ(2)-ρ(1))/(ρ(1)+ρ(2)) ranging from 2.45×10(-3) to 4.0×10(-3), where (ρ(1),ρ(2)) are the initial densities of the two fluids, with multiple cycles observed at At=2.55×10(-3). The evolution of the density and velocity fields in these flows was measured simultaneously using laser-induced fluorescence and particle image velocimetry. During each laminar-turbulent cycle, the axial velocity exhibits a distinctive ramp-cliff pattern, indicating that the flow accelerates as it relaminarizes, then decelerates rapidly as the Kelvin-Helmholtz billows break down. Within the range of experimental conditions, transverse stratification does not directly determine the onset of instability. Instead, the data suggest that a necessary criterion for the onset of instability is for the local Reynolds number to exceed 2200, with only a weak dependence on the Richardson number.