Essential oils (EOs) have long been studied for their antimicrobial properties, yet most investigations rely on simplistic models, limited strain panels, and anecdotal interpretations - failing to meet the standards expected of modern anti-infective agents. Advancing beyond this tradition, we implement a framework developed over several years of systematic investigation. Using this approach, we assessed the antibiofilm activity of Rosmarinus officinalis L. and Thymus vulgaris L. EOs against a panel of clinical Staphylococcus aureus isolates obtained from non-healing wounds. By applying infection-relevant conditions, such as wound-mimicking media and surfaces, strain-level resolution, and both contact and volatile exposure, we revealed substantial inter-strain variability in susceptibility, challenging the notion of EOs as uniformly effective agents. This variability was quantified using robust statistics, lending confidence to the reproducibility and translational relevance of the findings. These results underscore the need for Essential Oil Stewardship: a reproducible, interdisciplinary framework for EO testing, interpretation, and clinical translation. Our work demonstrates that such approach is feasible and sets the foundation for its broader adoption. The key message from this study is that EOs cannot meaningfully support or complement antibiotics and antiseptic agents in combating infections unless they are evaluated with the same methodological rigor.