We introduce an optimisation methodology for maximising secondary particle and radiation yields from laser-plasma accelerators. The approach is demonstrated using the recently proposed pump-depletion-dominated laser wakefield acceleration regime (Horný et al 2024 Phys. Rev. E110 035202) as a reference case. Particle-in-cell simulations of a 6 fs, 1.5 J laser pulse driving a plasma accelerator are coupled to FLUKA Monte Carlo modelling of a tungsten converter in a two-stage workflow. Systematic scans of plasma length and converter thickness are combined with three optimisation algorithms, benchmarked against a conventional grid search. The methodology improves both accuracy and computational efficiency, offering a robust framework for tuning secondary sources. For the reference configuration, we obtain peak values of neutrons per shot (detected immediately behind the converter) and ∼0.49 J of total photon energy, highlighting strong prospects for high-repetition-rate operation.