We report results of a unprecedentedly deep, blind search for Ly-alpha emitters (LAEs) at z = 5.7 using IMACS, the Inamori-Magellan Areal Camera & Spectrograph, with the goal of identifying missing sources of reionization that could also be basic building blocks for todays L* galaxies. We describe how improvements in wide field imaging with the Baade telescope, upgrades to IMACS, and the accumulation of ~20 hours of integration per field in excellent seeing led to the detection of single-emission-line sources as faint as F ~ 2 x 10^{-18} ergs s^{-1} cm^{-2}, a sensitivity 5 times deeper than our first search (Martin et al. 2008). A reasonable correction for foreground interlopers implies a steep rise of approximately an order of magnitude in source density for a factor of four drop in flux, from F = 10^{-17.0} ergs s^{-1} cm^{-2} to F = 10^{-17.6} (2.5) x 10^{-18} ergs s^{-1} cm^{-2}. At this flux the putative LAEs have reached a surface density of ~1 per sq arcminute -- a comoving volume density of 4 x 10^{-3} Mpc^{-3}, several times the density of L* galaxies today. Such a population of faint LAEs would account for a significant fraction of the critical flux density required to complete reionization at this epoch, and would be good candidates for building blocks of stellar mass ~10^{8-9} Msun for the young galaxies of this epoch.