A large-scale MIMO (multiple-input multiple-output) system offers significant advantages in wireless communication, including potential spatial multiplexing and beamforming capabilities. However, channel estimation becomes challenging with multiple antennas at both the transmitter and receiver ends. The minimum mean-squared error (MMSE) estimator, for instance, requires a spatial correlation matrix whose dimensions scale with the square of the product of the number of antennas on the transmitter and receiver sides. This scaling presents a substantial challenge, particularly as antenna counts increase in line with current technological trends. Traditional MIMO literature offers alternative channel estimators that mitigate the need to fully acquire the spatial correlation matrix. In this paper, we revisit point-to-point MIMO channel estimation and introduce a reduced-subspace least squares (RS-LS) channel estimator designed to eliminate physically impossible channel dimensions inherent in uniform planar arrays. Additionally, we propose a cluster-aware RS-LS estimator that leverages both reduced and cluster-specific subspace properties, significantly enhancing performance over the conventional RS-LS approach. Notably, both proposed methods obviate the need for fully/partial knowledge of the spatial correlation matrix.