Since the discovery of two-dimensional electron gas (2DEG) at the oxide interface of LaAlO3/SrTiO3 (LAO/STO), improving carrier mobility has become an important issue for device applications. In this paper, by using an alternate polar perovskite insulator (La0.3Sr0.7) (Al0.65Ta0.35)O3 (LSAT) for reducing lattice mismatch from 3.0% to 1.0%, the low-temperature carrier mobility has been increased 30 fold to 35 000 cm2 V-1 s-1. Moreover, two critical thicknesses for the LSAT/STO (001) interface are found, one at 5 unit cells for appearance of the 2DEG and the other at 12 unit cells for a peak in the carrier mobility. By contrast, the conducting (110) and (111) LSAT/STO interfaces only show a single critical thickness of 8 unit cells. This can be explained in terms of polar fluctuation arising from LSAT chemical composition. In addition to lattice mismatch and crystal symmetry at the interface, polar fluctuation arising from composition has been identified as an important variable to be tailored at the oxide interfaces to optimize the 2DEG transport.