What is the safest, most effective way to cleave through thick bone?
The most reliable technique I found was the following:


Hold the cleaver in your left hand (assuming you are right-handed);
Press the cleaver from the top with your right hand to make a slight indentation into the bone, in order to maintain a stable hold for the next step;
Use a wooden mallet to pound the flat (top) end of the cleaver, again with your right hand.


This is completely safe and doesn't require precise aim.  Usually even the thickest bones can be cleaved through completely with 2 or 3 hard whacks from the mallet.