Measurements of photon-number-dependent time-of-arrival (TOA) distributions in wide NbN superconducting microstrip single-photon detectors (SMSPDs) are presented. Two 10um-long devices with widths of 3.2um and 6.4um are characterized under pulsed 515nm excitation. The TOA histograms are described by sums of exponentially modified Gaussian (EMG) components, with the wider device exhibiting components assigned to photon numbers up to n=8. Adjacent TOA peaks become more distinguishable relative to their widths at higher photon number, in contrast to the compression of neighboring photon-number timing shifts observed in conventional narrow-wire SNSPDs. For the components assigned to n=7 and n=8, the FWHM-normalized peak separation is 2.15, and the fitted EMG distributions yield an equal-prior pairwise TOA-assignment fidelity of 99.6%. The EMG exponential-tail parameter τₙ decreases strongly with photon number, while the Gaussian-location parameter μₙ continues to shift between neighboring components. A phenomenological model motivated by absorption-site-dependent vortex processes and collective current redistribution captures these timing trends. These results support wide SMSPDs as a platform for TOA-based photon-number discrimination at high photon number, relevant to multiphoton-state characterization and photonic quantum information processing. The same geometry also provides a setting to examine how the spatial distribution of photon absorption affects vortex-assisted detection.