I've found a bug report which includes a workaround that works!
See here: https://github.com/Leaflet/Leaflet/issues/2693
Specifically, you need to add a bit of code:
map.on('zoomanim', debounce(map._onZoomTransitionEnd, 250));
The debounce function can be found here: http://davidwalsh.name/javascript-debounce-function