  In a prior work, the authors proved a global bifurcation theorem for
spatially periodic interfacial hydroelastic traveling waves on infinite depth,
and computed such traveling waves. The formulation of the traveling wave
problem used both analytically and numerically allows for waves with
multi-valued height. The global bifurcation theorem required a one-dimensional
kernel in the linearization of the relevant mapping, but for some parameter
values, the kernel is instead two-dimensional. In the present work, we study
these cases with two-dimensional kernels, which occur in resonant and
non-resonant variants. We apply an implicit function theorem argument to prove
existence of traveling waves in both of these situations. We compute the waves
numerically as well, in both the resonant and non-resonant cases.
