Well i think i will upset a few people with this statement.
Backlash compensation works in theory but not in the real world cutting difficult materials.
Why do you think quality builders put so much effort in to an engineering solution to backlash.
When conventional milling the axis motor power is being used to drive the cutter in the cutting process.
In climb milling the axis motor is being used to prevent the cutting axis being drawn into the workpiece
So when you are climb milling with the backlash hidden with compensation the cutter is being drawn into the workpiece unexpectedly this results in a sudden overload of cutting depth which results in you going off the toolpath appearing to be lost steps. This is probably why you broke a cutter.
So the answer is simple to fix your problem fix the mechanical backlash.
Phil