  Bosonic and RNS chiral strings have been defined from a singular gauge fixing
of the respective Polyakov and spinning string actions, enforcing, among other
things, the finite nature of their physical spectra. Except for the heterotic
case, the tensionless limits of such chiral models have been shown to describe
the same field theories predicted by their ambitwistor analogues. In this
paper, we study the Green-Schwarz formulation for Type II and heterotic
superstrings in a singular gauge. After performing a light-cone gauge analysis,
their physical spectra are shown to match those of RNS chiral strings, and
their respective tensionless limits are found to describe the same field
theories predicted by RNS ambitwistor strings. Their pure spinor counterparts
are then introduced by making use of the Oda-Tonin method. In doing so,
symmetries hidden in the pure spinor ambitwistor string action become manifest,
proposals motivating the sectorized pure spinor BRST charges find simple
grounds, and integrated vertex operators emerge naturally.
