In orthogonal frequency-division multiplexing-based radar and integrated sensing and communication systems, the sensing range is traditionally limited by the round-trip time corresponding to the cyclic prefix duration. Targets whose echoes arrive after this duration induce intersymbol interference (ISI) and associated intercarrier interference (ICI), which significantly degrade detection performance, elevate the interference-noise floor in the radar image, and reduce the useful signal power due to window mismatch. Existing methods face a trade-off between recovering useful signal and suppressing interference, particularly in multi-target scenarios. This paper proposes two frameworks to resolve this dilemma, offering a flexible trade-off between computational cost and target detection performance. First, a signal model is derived, demonstrating that ISI and ICI-oriented interference often dominates thermal noise in high-dynamic-range scenarios. To combat the ISI and ICI-based interference-noise floor increase, joint-interference cancellation with coherent compensation is proposed. This approach is an efficient evolution of the successive-interference cancellation algorithm, utilizing high-precision chirp Z-transform estimation and frequency-domain coherent compensation to recover weak distant targets. For scenarios requiring maximum precision, the full reconstruction-based sliding window scheme is presented, which shifts the receive window to capture optimal signal energy while performing full-signal reconstruction for all detected targets. Numerical results show that both methods outperform state-of-the-art benchmarks.