  We present new developments and comparisons of competing inspiral and
waveform models for highly eccentric non-spinning extreme and intermediate
mass-ratio inspirals (EMRIs and IMRIs). Starting from our high eccentricity
self-force library, we apply the near-identity transform (NIT) technique to
rapidly compute highly eccentric self-forced inspirals for the first time. Upon
evaluating our approximate NIT results via comparison with full self-force
inspirals, we couple our accurate and streamlined inspiral data to potential
waveform generation schemes. We find that, although high eccentricity strains
the NIT method, NIT inspirals are consistent with full self-force inspirals for
EMRIs. However, our NIT implementation (at 1st post-adiabatic order) is not
able to achieve LISA-motivated accuracy goals for highly eccentric IMRIs. Our
most sophisticated waveforms are devised through a new technique that
efficiently connects NIT orbital parameters to Teukolsky amplitudes and phases.
We compare these sophisticated Teukolsky waveforms to those with synthesized
(summing over harmonics) amplitudes based on a kludge. We find that, assuming
identical worldlines (so that dephasing is negligible), kludge waveforms
compare favorably to Teukolsky waveforms for non-spinning bodies.
