Conceptual rainfall–runoff models retain antecedent information through dynamic states, but differ in whether individual runoff-generation contributions are distributed over subsequent time steps. GRHyMoLAP represents antecedent influence through its production store and recession dynamics, yet applies its additive runoff-generation forcing instantaneously. We introduce mGRHyMoLAP, which replaces this instantaneous application with a normalized temporal convolution while retaining the original storage and recession structure. We represent different temporal convolution shapes by comparing a flexible discrete kernel with parsimonious exponential and log-normal kernels and testing them out of sample across 623 CAMELS-GB catchments against the original GRHyMoLAP and GR4J. The log-normal formulation improves NSE in 93.1% and KGE in 90.7% of catchments relative to GRHyMoLAP and outperforms GR4J in 68.1% and 72.6%, respectively. Beyond aggregate performance, mGRHyMoLAP maintains similar agreement during non-increasing-flow periods while more consistently reproducing the observed direction of daily flow increases. Extending the kernel from current-day forcing only to include one antecedent day captures most of the performance gain, with little further median improvement for longer memory windows. A non-zero kernel peak occurs in 42.9% of catchments, indicating a substantial contribution of antecedent runoff-generation forcing; 96.6% of these catchments peak at a lag of one day. All catchments with a non-zero lag peak improve relative to GRHyMoLAP, with a median NSE increase of 0.067, compared with improvements in 87.9% and a median increase of 0.010 among catchments with a lag-0 peak. Simulated performance is robust across calibration choices, whereas detailed kernel moments and tails are less identifiable, supporting peak lag as the primary diagnostic while cautioning against interpreting the calibrated kernel as a direct estimate of physical travel-time distributions. Non-zero peak lags are associated with larger catchments, longer high-flow durations, lower mean precipitation, higher aridity, and greater cropland fractions. These results demonstrate that temporal redistribution of runoff-generation forcing can improve GRHyMoLAP predictions and provide a useful model-based diagnostic of where such additional temporal flexibility is beneficial.