We report on a theoretical investigation of artificial spin-ice dipolar arrays using a nanoisland shape adopted from recent experiments (Farhan et al 2013 Nature Phys. 9 375). The number of thermal magnetic string excitations in the square lattice is drastically increased by a vertical displacement of rows and columns. We find large increments especially for low temperatures and for string excitations with quasi-monopoles of charges ± 4. By kinetic Monte Carlo simulations we address the thermal stability of such excitations, thereby providing time scales for their experimental observation.