I recently visited Caltech to work with Alvin Chua (and Michael Katz, who was also visiting) on a new fast method to compute full relativistic EMRI waveforms that can incorporate all known self-force corrections to the phase. We made great progress during the week and are now writing up that work. I’ll post on that again when the paper is out.
Whilst at Caltech I gave a talk on our recent second-order in the mass-ratio result. That talk was recorded in case you are interested: