I'll add some of my own experience here, for which we are currently in the process of journal submission. I can't share the full abstract quite yet, but the very short version is that we tested list randomization in KwaZulu-Natal against both direct questionnaires, and more importantly, against known truths (HIV status, acquired by linkage with a local surveillance system). The list randomization arm not only did not improve upon direct questionnaires, but it performed much worse for some questions, even among those who definitively knew their own status. We think we know roughly why it performed so poorly, and it may be fixable, but that should help add a bit of caution.
List randomization, it seems, is not quite ready for prime time, and I would urge caution until we better research and understand best practices.