We carefully investigate three important effects including postgrowth activation annealing, delta ({delta}) dose and p+-GaN layer thickness and experimentally demonstrate their influence on the electrical properties of GaN p-n homojunction diodes with a tunnel junction (TJ)-based p-contact. The p-n diodes and TJ structures were monolithically grown by metalorganic chemical vapor deposition (MOCVD) in a single growth step. By optimizing the annealing time and temperature for magnesium (Mg) activation and introducing {delta}-doses for both donors and acceptors at TJ interfaces, a significant improvement in electrical properties is achieved. For the continuously-grown, all-MOCVD GaN homojunction TJs, ultra-low forward voltage penalties of 158 mV and 490 mV are obtained at current densities of 20 A/cm2 and 100 A/cm2, respectively. The p-n diode with an engineered TJ shows a record-low normalized differential resistance of 1.6 x 10-4 {Omega}-cm2 at 5 kA/cm2.