The use of kinetic models of metabolism in design-build-learn-test cycles is limited despite their potential to guide and accelerate the optimization of cell factories. This is primarily due to difficulties in constructing kinetic models capable of capturing the complexities of the fermentation conditions. Building on recent advances in kinetic-model-based strain design, we present the rational metabolic engineering of an S. cerevisiae strain designed to overproduce p-coumaric acid (p-CA), an aromatic amino acid with valuable nutritional and therapeutic applications. To this end, we built nine kinetic models of an already engineered p-CA-producing strain by integrating different types of omics data and imposing physiological constraints pertinent to the strain. These nine models contained 268 mass balances involved in 303 reactions across four compartments and could reproduce the dynamic characteristics of the strain in batch fermentation simulations. We used constraint-based metabolic control analysis to generate combinatorial designs of 3 enzyme manipulations that could increase p-CA yield on glucose while ensuring that the resulting engineering strains did not deviate far from the reference phenotype. Among 39 unique designs, 10 proved robust across the phenotypic uncertainty of the models and could reliably increase p-CA yield in nonlinear simulations. We implemented these top 10 designs in a batch fermentation setting using a promoter-swapping strategy for down-regulations and plasmids for up-regulations. Eight out of the ten designs produced higher p-CA titers than the reference strain, with 19-32% increases at the end of fermentation. All eight designs also maintained at least 90% of the reference strain's growth rate, indicating the critical role of the phenotypic constraint. The high experimental success of our in-silico predictions lays the foundation for accelerated design-build-test-learn cycles enabled by large-scale kinetic modeling.