To address complex problems, scholars are increasingly faced with challenges of integrating diverse knowledge domains. We analyzed the evolution of this convergence paradigm in the broad ecosystem of brain science, which provides a real-time testbed for evaluating two modes of cross-domain integration - subject area exploration via expansive learning and cross-disciplinary collaboration among domain experts. We show that research involving both modes features a 16% citation premium relative to a mono-disciplinary baseline. Further comparison of research integrating neighboring versus distant research domains shows that the cross-disciplinary mode is essential for integrating across relatively large disciplinary distances. Yet we find research utilizing cross-domain subject area exploration alone - a convergence shortcut - to be growing in prevalence at roughly 3% per year, significantly faster than the alternative cross-disciplinary mode, despite being less effective at integrating domains and markedly less impactful. By measuring shifts in the prevalence and impact of different convergence modes in the 5-year intervals before and after 2013, our results indicate that these counterproductive patterns may relate to competitive pressures associated with global Human Brain flagship funding initiatives. Without additional policy guidance, such Grand Challenge flagships may unintentionally incentivize such convergence shortcuts, thereby undercutting the advantages of cross-disciplinary teams in tackling challenges calling on convergence.