Current crowding close to electrical contacts is a common challenge in all optoelectronic devices containing thin current spreading layers (CSLs). We analyze the effects of current spreading on the operation of the so-called double diode structure (DDS), consisting of a light emitting diode (LED) and a photodiode (PD) fabricated within the same epitaxial growth process, and providing an attractive platform for studying electroluminescent (EL) cooling under high bias conditions. We show that current spreading in the common n-type layer between the LED and the PD can be dramatically improved by the strong optical coupling between the diodes, as the coupling enables a photo-generated current through the PD. This reduces the current in the DDS CSL and enables the study of EL cooling using structures that are not limited by the conventional light extraction challenges encountered in normal LEDs. The current spreading in the structures is studied using optical imaging techniques, electrical measurements, simulations, as well as simple equivalent circuit models developed for this purpose. The improved current spreading leads further to a mutual dependence with the coupling efficiency, which is expected to facilitate the process of optimizing the DDS. We also report a new improved value of 63% for the DDS coupling quantum efficiency.