We investigate polyelectrolyte bridging interactions mediated by charged, flexible, polyelectrolyte chains between fixed cylindrical macroions of opposite charge in a two-dimensional hexagonal crystalline array. We show that in the asymptotic regime of small macroion density, the polyelectrolyte-mediated attraction is long range, falling off approximately linearly with the macroion array density. We investigate the polyelectrolyte free energy as a function of the macroion density and derive several analytic limiting laws valid in different regimes of the parameter space.