Ion cyclotron emission (ICE) driven by perpendicular neutral beam-injected (NBI) deuterons, together with the distinctive ICE driven by tangential NBI, have been observed from heliotron-stellarator plasmas in the Large Helical Device (LHD). Radio frequency radiation in the lower hybrid range has also been observed, with frequency dependent on plasma density. Here we focus on recent measurements of ICE from deuterium plasmas in LHD, which show substantial variation in spectral character, between otherwise similar plasmas that have different local density in the emitting region. Here we analyse this variation by means of first principles simulations, carried out using a particle-in-cell (PIC) kinetic approach. We show, first, that this ICE is driven by perpendicular NBI deuterons, freshly ionised near their injection point in the outer midplane edge of LHD. We find that these NBI deuterons undergo collective sub-Alfvénic relaxation, which we follow deep into the nonlinear phase of the magnetoacoustic cyclotron instability. The frequency and wavenumber dependence of the saturated amplitudes of the excited fields determine our simulated ICE spectra, and these spectra are obtained for different local densities corresponding to the different LHD ICE-emitting plasmas. The variation with density of the spectral character of the simulated ICE corresponds well with that of the observed ICE from LHD. These results from heliotron-stellarator plasmas complement recent studies of density-dependent ICE from tokamak plasmas in KSTAR [2, 3], where the spectra vary on sub-microsecond timescales after an ELM crash. Taken together, these results confirm the strongly spatially localised character of ICE physics, and reinforce the potential of ICE as a diagnostic of energetic ion populations and of the ambient plasma.