We present an analysis of the most extensive explicit-solvent simulations of β-hairpins to date (9.4 ms in aggregate), with the aim of probing the effects of tryptophan mutations on folding. From molecular simulations of GB1 hairpin, trpzip4, trpzip5, and trpzip6 performed on Folding@home, Markov State Models (MSMs) were constructed using a unified set of metastable states, enabling objective comparison of folding mechanisms. MSM models display quantitative agreement with experimental structural observables and folding kinetics, and predict multimodal kinetics due to specific non-native kinetic traps, which be identified as on- or off-pathway from the network topology. We quantify kinetic frustration by several means, including the s-ensemble method to evaluate glasslike behavior. Free-energy profiles and transition state movement clearly show stabilization of non-native states as Trp mutations are introduced. Remarkably, we find that "β-capped" sequences (trpzip4 and trpzip5) are able to overcome this frustration and remain cooperative two-state folders with a large time-scale gap. These results suggest that, while β-capping motifs are robust, fold stabilization by tryptophan generally may require overcoming significant non-native kinetic traps, perhaps explaining their under-representation in natural proteins.