I am proposing a multilevel mixture model to compare them.

Ok. You can use whatever statistical model you want, as long as we are clear what the underlying object is you are dealing with. The difficulty here isn't the statistical modeling, but being clear about what it is that is being estimated (in other words the interpretation of the parameters of the model). This is why I don't talk about statistical modeling at first.

haven't seen any intervention-style algorithms which work with just the effect sizes which is what is on offer.

If all you have is reported effect sizes you won't get anything good out. You need the data they used.