Crowdsourcing is a popular tool for collecting large amounts of annotated data, but the specific format of the strong labels necessary for sound event detection is not easily obtainable through crowdsourcing. In this work, we propose a novel annotation workflow that leverages the efficiency of crowdsourcing weak labels, and uses a high number of annotators to produce reliable and objective strong labels. The weak labels are collected in a highly redundant setup, to allow reconstruction of the temporal information. To obtain reliable labels, the annotators' competence is estimated using MACE (Multi-Annotator Competence Estimation) and incorporated into the strong labels estimation through weighing of individual opinions. We show that the proposed method produces consistently reliable strong annotations not only for synthetic audio mixtures, but also for audio recordings of real everyday environments. While only a maximum 80% coincidence with the complete and correct reference annotations was obtained for synthetic data, these results are explained by an extended study of how polyphony and SNR levels affect the identification rate of the sound events by the annotators. On real data, even though the estimated annotators' competence is significantly lower and the coincidence with reference labels is under 69%, the proposed majority opinion approach produces reliable aggregated strong labels in comparison with the more difficult task of crowdsourcing directly strong labels.