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.
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