One thing to take into consideration would be the helix angle of the threads.
You state that cutting RH threads are no problem with the current tool, well this should be the case as the geometry is setup to get the correct response.
When cutting the LH thread the tool may be rubbing, thus causing the "deflection" and inconsistent sizing.
I would suggest that if you are planning on doing lots of LH threads, that you invest in a threading bar that is designed to cut LH threads. It will save you a truck load of grief!
You may be lucky enough that all you need to do is to change the shim in your tool.
I hope so, will be much cheaper.
Check with your tool supplier. They are always my point of call when having trouble like you state.