Electrically pumped random lasers with distributed feedback can be obtained by introducing random defects into the device active layer, modifying the epitaxial growth process and losing the ease of fabrication potentially offered by disordered structures. We recently demonstrated an alternative and more practical approach in which random lasing emission is obtained from a modified Fabry-Perot laser diode after pulsed laser ablation of its output mirror. Here, we improve our fabrication technique by sweeping the ablating laser beam along the output mirror at different speeds and with different pulse energies, obtaining control over the total energy delivered at each point. We optimize the ablation parameters by evaluating the device performances in terms of lasing threshold and output power and we present the device emission characteristics. The proposed technique is tunable, fast and reliable, allowing the fabrication of devices with different properties by proper selection of the ablation parameters.