Labradorite is a type of Feldspar and has natural cleavage planes that make it very difficult to work.
You may be able to support the front by embedding it in something, plaster is what I was thinking but it would be a pain to remove the plaster and possibly lead to breaking the rock you have just spent hours on.
If you can come up with something to support the front then I would grind the back down by hand working on a steel plate and using loose Silicon Carbide grit slurry.
Thinking about this I wonder if doping wax would work, then just immerse stone, wax and whatever in metho until the wax dissolves.