  In this paper we begin revisiting the little string theories (LSTs) which
govern the dynamics of the instantonic heterotic $E_8 \times E_8$ five-branes
probing ALE singularities, building on and extending previous results on the
subject by Aspinwall and Morrison as well as Blum and Intriligator. Our focus
are the cases corresponding to choices of non-trivial flat connections at
infinity. The latter are in particular interesting for the exceptional ALE
singularities, where a brane realization in Type I$'$ is lacking. Our approach
to determine these models is based on 6d conformal matter: we determine these
theories as generalized 6d quivers. All these LSTs have a higher-one form
symmetry which forms a 2-group with the zero-form Poincar\'e symmetry, the
R-symmetry and the other global symmetries: the matching of the R-symmetry
two-group structure constant is a stringent constraint for T-dualities, which
we use in combination with the matching of 5d Coulomb branches and flavor
symmetries upon circle reduction, as a consistency check for the realization of
the 6d LSTs we propose.
