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The observed spectral lags of gamma-ray bursts (GRBs) have been widely used to explore possible violations of Lorentz invariance. However, these studies were generally performed by concentrating on the rough time lag of a single highest-energy photon and ignoring the intrinsic time lag at the source. A new way to test nonbirefringent Lorentz-violating effects has been proposed by analyzing the multi-photon spectral-lag behavior of a GRB that displays a positive-to-negative transition. This method gives both a plausible description of the intrinsic energy-dependent time lag and comparatively robust constraints on Lorentz-violating effects. In this work, we conduct a systematic search for Lorentz-violating photon dispersion from the spectral-lag transition features of 32 GRBs. By fitting the spectral-lag data of these 32 GRBs, we place constraints on a variety of isotropic and anisotropic Lorentz-violating coefficients with mass dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mn>6</mn></mrow></semantics></math></inline-formula> and 8. While our dispersion constraints are not competitive with existing bounds, they have the promise to complement the full coefficient space.