We present results from a continuing interferometric survey of high-redshift submillimeter galaxies with the Submillimeter Array, including high-resolution (beam size ∼ 2 arcsec) imaging of eight additional AzTEC 1.1mm selected sources in the COSMOS Field, for which we obtain six reliable (peak S/N > 5 or peak S/N > 4 with multiwavelength counterparts within the beam) and two moderate significance (peak S/N > 4) detections. When combined with previous detections, this yields an unbiased sample of millimeter-selected SMGs with complete interferometric followup. With this sample in hand, we (1) empirically confirm the radio-submillimeter association, (2) examine the submillimeter morphology – including the nature of submillimeter galaxies with multiple radio counterparts and constraints on the physical scale of the far infrared – of the sample, and (3) find additional evidence for a population of extremely luminous, radio-dim submillimeter galaxies that peaks at higher redshift than previous, radio-selected samples. In particular, the presence of such a population of high-redshift sources has important consequences for models of galaxy formation – which struggle to account for such objects even under liberal assumptions – and dust production models given the limited time since the Big Bang.