The prospects for glider-based measurement of turbulence statistics are assessed using direct numerical simulation data representing breaking Kelvin-Helmholtz (KH) billows in a stratified, parallel shear flow. Transects tilted upstream against the shear tend to produce overestimates of overturning; those tilted with the shear produce underestimates. Low-angle transects can produce illusory overturning as the braid between the KH billows is crossed. Statistical features of the bias in displacement scales are related to geometrical aspects of KH billows. Results are interpreted in the context of a hypothetical effort to characterize overturning in a strongly sheared current (e.g. the Equatorial Undercurrent) using nonvertical profiles.