Previous work has shown that Spectrally Efficient Frequency Division Multiplexing (SEFDM) systems yield up to 40% bandwidth savings at the expense of receiver complexity. Maximum Likelihood (ML) and Sphere Decoding (SD) suffer from an impractical computational complexity. Hybrid detectors, such as Truncated Singular Value Decomposition (TSVD) with fixed complexity SD offer a notable reduction in complexity while maintaining an acceptable error performance. Yet, for high-dimensional systems, even these reduced complexity detectors present challenges for implementation. Hence, in this work, we apply Sort-Free (SF) and Modified Real Valued Decomposition (MRVD) techniques to obtain targeted reduction in computational complexity and improved error performance. Our findings are validated via simulation and practical experimentation with the aid of a Digital Signal Processor (DSP) chip.