They changed the convention of having different basis types for each hand in the Orion C# library. I'm not actually sure whether this was changed for the JSON data coming from the web socket or not. If you download the Leap Motion SDK (not the Unity assets), you can look at the C# source code. If you look in the ServiceFrameFactory class, you can see how all the hands are built -- from structs marshaled from C in this case. This won't have a basis conversion for the right/left hand issue, but that is just a matter of changing a sign of one of the basis vectors (or two), if I recall correctly.
Note that I'm no longer with Leap Motion, so I won't be able to provide any further assistance. Good luck!