This paper presents a direct transcription frame-work for optimising the operation of gyroscope-based iner-tial wave energy harvesters (WEH). In contrast to currently adopted procedures, we introduce a tailored optimal map as part of the total flywheel speed of the WEH, designed to maximise energy absorption. Since the target optimisation problem is infinite-dimensional, we derive a direct transcription process accordingly, exploiting tools from the field of moment-based theory. Following a formal derivation, the proposed framework is applied to a gyropendulum - based system, offering a numerical appraisal of the main characteristics underlying the methodology. We show that the procedure offered within this study is able to significantly enhance power absorption, hence contributing towards optimal energy-maximising operation of this family of systems.