Electrical conductivity relaxation is used for monitoring the cubic-to-hexagonal phase transition in the perovskite-type oxide Ba0.5Sr0.5Co0.8Fe0.2O3-delta. After in situ annealing at 1173 K, at which temperature the cubic polymorph is stable, electrical conductivity relaxation experiments are conducted during long-term annealing at 1073 K. The decreases in the surface exchange and chemical diffusion coefficients with time due to the sluggish phase transition are found to be correlated. It is demonstrated that B-site doping with Zr to an amount as low as 3 mol % stabilizes the high-temperature perovskite cubic phase of Ba0.5Sr0.5Co0.8Fe0.2O3-delta, with preservation of its high oxygen transport and exchange properties.