High-power, continuously tunable terahertz sources based on free-electron lasers require precise control of electron-beam microstructures. Quantitative prediction of the modulation amplitude across a broad frequency range remains challenging because the laser-induced distribution and its collective evolution must be treated together. To describe this coupled evolution, a nonlinear model is developed for microbunching seeded by a frequency-beating laser heater. The non-Gaussian heater-exit distribution is obtained by optical phase averaging and propagated through multistage compression in six-dimensional phase space. Source-induced correlations are retained, with space charge, coherent synchrotron radiation, and radio-frequency wakefields evaluated self-consistently. The wavelength-dependent bunching response is thereby connected to the laser beat frequency, laser power, and compression partition. The short-wavelength double peak is found to be governed mainly by longitudinal space charge, while bunching near a selected wavelength can be enhanced by redistributing compression at fixed total compression. The predicted source modulation and downstream response are benchmarked against Elegant and IMPACT-Z, respectively. Experimental measurements of the wavelength-dependent bunching factor at different laser pulse energies are found to agree well with the trends predicted by theory and simulation. The resulting framework provides a computationally efficient and predictive route to optimizing electron-beam microbunching for tunable, high-power terahertz generation at free-electron-laser facilities.