Large-Area Electronics (LAE) technology has enabled the development of physically-expansive sensing systems with a flexible form-factor, including large-aperture microphone arrays. We propose an approach to blind source separation based on leveraging such an array. In our algorithm we carry out delay-sum beamforming, but use frequency-dependent time delays, making it well-suited for a practical reverberant room. This is followed by a binary mask stage for further interference cancellation. A key feature is that it is fully «blind», since it requires no prior information about the location of the speakers or microphones. Instead, we carry out k-means cluster analysis, to estimate time delays in the background from acquired audio signals that represent the mixture of simultaneous sources. We have tested this algorithm in a conference room (T60 = 350 ms), using two linear arrays consisting of: (1) commercial electret capsules, and (2) LAE microphones, fabricated in-house. We have achieved high-quality separation results, obtaining a mean PESQ MOS improvement (relative to the unprocessed signal) for the electret array of 0.7 for two sources and 0.6 for four simultaneous sources, and for the LAE array of 0.5 and 0.3, respectively.