  Realizing the potential of 21 cm tomography to statistically probe the
intergalactic medium before and during the Epoch of Reionization requires large
telescopes and precise control of systematics. Next-generation telescopes are
now being designed and built to meet these challenges, drawing lessons from
first-generation experiments that showed the benefits of densely packed, highly
redundant arrays--in which the same mode on the sky is sampled by many antenna
pairs--for achieving high sensitivity, precise calibration, and robust
foreground mitigation. In this work, we focus on the Hydrogen Epoch of
Reionization Array (HERA) as an interferometer with a dense, redundant core
designed following these lessons to be optimized for 21 cm cosmology. We show
how modestly supplementing or modifying a compact design like HERA's can still
deliver high sensitivity while enhancing strategies for calibration and
foreground mitigation. In particular, we compare the imaging capability of
several array configurations, both instantaneously (to address instrumental and
ionospheric effects) and with rotation synthesis (for foreground removal). We
also examine the effects that configuration has on calibratability using
instantaneous redundancy. We find that improved imaging with sub-aperture
sampling via "off-grid" antennas and increased angular resolution via far-flung
"outrigger" antennas is possible with a redundantly calibratable array
configuration.
