Try the carrot, but have the stick ready, we all know who the main offenders are, we need to have a bit of vigilantism in a nice way to give some fearless feedback.
If there are some ‘main offenders’ then speak to them, or arrange communication some other way. A reverse rota won’t help in this, plus it has the effect of a few signing up and doing cleaning/clearing that others could easily do as they go.
It was discussed a few weeks back about whether to have these reverse rotas in each area: the idea then was not to clear up after other people who had left mess, but to do the tasks that are a bit wider: cleaning the sink and taps, cleaning the fridge, hoovering social, sweeping whole floor. These all need doing but aren’t part of ‘clear up after yourself’.