We analyze the phenomenology of a simplified model for a real scalar dark matter candidate interacting with quarks via a coloured fermionic mediator. In the coannihilation regime, the dark matter abundance is controlled by the dynamics of the coloured fermions which can be significantly affected by non-perturbative effects. We employ a non-relativistic effective field theory which allows us to systematically treat the Sommerfeld effect and bound state formation in the early Universe. The parameter space compatible with the dark matter relic abundance is confronted with direct, indirect and collider searches. A substantial part of the parameter space, with dark matter masses up to 18 TeV, is already excluded by XENON1T. Most of the remaining thermal relics can be probed by a future Darwin-like experiments, when taking properly into account the running of the relevant couplings for the direct detection processes.