This paper presents novel algorithms for multi-target direction-of-arrival (DoA) estimation in array signal processing. Although the maximum likelihood estimator (MLE) asymptotically attains the Cramér-Rao bound, its exponential complexity motivates practical alternatives, such as greedy or subspace-based methods. In this context, greedy methods such as orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are sensitive to early selection errors, especially for angularly proximate targets, whereas subspace-based methods such as multiple signal classification (MUSIC) present angular super-resolution capabilities but degrade under strong inter-target signal correlation. To overcome these limitations, we propose two greedy iterative MUSIC (G-iMUSIC) algorithms, namely OMP-iMUSIC and OLS-iMUSIC, derived from a unified framework that links subspace and greedy estimations. Unlike prior iMUSIC approaches, the proposed methods require only one initial eigen value decomposition (EVD) and avoid computing eigendecomposition at each iteration. They also admit Fast Fourier Transform (FFT)-accelerated implementations for uniform linear arrays (ULAs), enabling low-complexity operation. Monte Carlo simulations demonstrate improved detection and precision over conventional OMP, OLS, and MUSIC, as well as reduced processing time compared to greedy baselines. Finally, we introduce diagnostic metrics that interpret performance across signal correlation and angular proximity regimes, supporting generalization beyond the specific orthogonal frequency-division multiplexing (OFDM) radar scenario considered.