In this work we report experimental results on optimizing the refractive index (RI) sensitivity of long-period gratings (LPGs) by fiber cladding etching and thin aluminum oxide (Al2O3) overlay deposition. The presented LPG takes advantage of work in the dispersion turning point (DTP) regime as well as the mode transition (MT) effect for higher-order cladding modes (LP09 and LP010). The MT was obtained by depositing Al2O3 overlays with single-nanometer precision using the Atomic Layer Deposition method (ALD). Etching of both the overlay and the fiber cladding was performed using hydrofluoric acid (HF). For shallow etching of the cladding, i.e., DTP observed at next = 1.429 and 1.439 RIU for an LPG with no overlay, followed by deposition of an overlay of up to 167 nm in thickness, HF etching allowed for post-deposition fine-tuning of the overlay thickness resulting in a significant increase in RI sensitivity mainly at the DTP of the LP09 cladding mode. However, at an external RI (next) above 1.39 RIU, the DTP of LP010 was noticed, and its RI sensitivity exceeded 9,000 nm/RIU. Deeper etching of the cladding, i.e., DTP observed for next above 1.45 RIU, followed by the deposition of thicker overlays (up to 201 nm in thickness) allowed the sensitivity to reach values of over 40,000 nm/RIU in a narrow RI range. Sensitivity exceeding 20,000 nm/RIU was obtained in an RI range suitable for label-free biosensing applications.