This paper presents a quasi-equilibrium growth (QEG) strategy for synthesizing inch-scale monolayer α-In₂Se₃ single crystals on fluor-phlogopite substrates. The QEG method effectively overcomes challenges associated with the small energy difference between locally stable orientations during growth, leading to robust single-orientation epitaxy. The high-quality single-crystal α-In₂Se₃ films exhibit high electron mobility (up to 117.2 cm²V⁻¹s⁻¹) and demonstrate reliable nonvolatile memory performance in ferroelectric field-effect transistors (Fe-FETs). This QEG method offers a promising route for producing large-area single-crystal 2D materials for applications in 2D ferroelectric devices and nanoelectronics.