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Experimental results, supported by precise modelling, demonstrate optimisation of a plasma-based injector with intermediate laser pulse energy ($<1$ J), corresponding to a normalised vector potential $a_0 = 2.15$, using ionisation injection in a tailored plasma density profile. An increase in electron bunch quality and energy is achieved experimentally with the extension of the density downramp at the plasma exit. Optimisation of the focal position of the laser pulse in the tailored plasma density profile is shown to efficiently reduce electron bunch angular deviation, leading to a better alignment of the electron bunch with the laser axis. Single peak electron spectra are produced in a previously unexplored regime by combining an early focal position and adaptive optic control of the laser wavefront through optimising the symmetry of the pre-focal laser energy distribution. Experimental results have been validated through particle-in-cell simulations using realistic laser energy, phase distribution, and temporal envelope, allowing for accurate predictions of difficult to model parameters, such as total charge and spatial properties of the electron bunches, opening the way for more accurate modelling for the design of plasma-based accelerators.