Don't sell it if you still love that watch. Bad things happen, even to higher tier watch as well.
Shouldn't be too hard finding and repairing parts of 1887.
Hmm, I would try at an AD or an independent watch repair centre that handles TAG Heuer's and has a parts account at LVMH to get a repair-quote first and decide what to do after that.
Anyways, succes with whatever decision you choose!