We have performed a search for neutrinoless β⁺EC decay of ¹²⁰Te using the final CUORE-0 data release. We describe a new analysis method for the simultaneous fit of signatures with different event topology, and of data subsets with different signal efficiency, obtaining a limit on the half-life of the decay of T_1/2 > 1.6 × 10²¹ yr at 90% CI. Combining this with results from Cuoricino, a predecessor experiment, we obtain the strongest limit to date, corresponding to T_1/2 > 2.7 × 10²¹ yr at 90% CI.