React listen for (virtual) DOM changes

I know this is not idiomatic React, but I'm working on a React component (an inverse scrollview) which needs to get notified of downstream virtual DOM changes both before they are rendered and after they are rendered.

This is a little hard to explain so I made a JSFiddle with a starting point: https://jsfiddle.net/7hwtxdap/2/

My goal is to have the log look like:

Begin log

render

rendered small

rendered small

rendered small

before update

rendered big

after update

before update

rendered big

after update

before update

rendered big

after update

I'm aware that React sometimes batches DOM changes and that's fine (i.e. the log events could be before update; rendered big; rendered big; after update; ...) -- important part is that I am actually notified before and after the DOM changes.