While I would fully support having Jaeger-Lecoultre overhaul the movement, cleaning and lubricating all that they can and replacing nothing but the most necessary mechanical components, I beg you, don't have them polish the case, refinish the dial or replace the hands. These show time in a very special way for you, and that is the point.
When I was in my early 20s, I had my grandfathers Girard-Perregaux and my father's Elgin refinished. I thought I was doing the right thing. Oh how I wish I could undo that decision.