We report room-temperature synthesis of lead- and iodide-deficient α-[HC(NH)]PbI perovskites (abbreviated d-α-FAPI, FA = formamidinium), with the general formula (A',FA)[PbI] (with A' = hydroxyethylammonium (HEA) or thioethylammonium (TEA) cations, 0.04 ≤ x ≤ 0.15). These materials retain a 3D character of their perovskite network despite incorporation of large HEA or TEA cations, demonstrating that the Goldschmidt tolerance factor can be bypassed. We found that thin films of (TEA,FA)[PbI] ( x = 0.04 and 0.13) show exceptional α-phase stability under ambient conditions, 1 order of magnitude higher than α-FAPI and α-(Cs,FA)PbI thin films. d-α-FAPI phases are shown to maintain a direct band gap, which increases monotonously for x ranging from 0 up to 0.20, with characteristics of a p-type semiconductor for low concentrations of vacancies ( x ≤ 0.13) and n-type for larger ones. They offer alternatives to reach the methylammonium- and bromine-free stable α-FAPI-type phase and open new avenues in the field of perovskite solar cells, up to band gap tuning desirable for tandem solar cells.