I would mostly actually be thinking of quite simple cases: we recruit a sample and have weights for each respondent. The repeated measures component might just be that we ask the same person multiple questions, and so we want to fit a random intercept for participant, as well as an effect of - for example - question framing.
I’ve confirmed that with my relatively simple approach above of just dividing by the design effect, it can correctly get at repeated measures effects but it would be nice to be able to do this with another package.