My idea on how to add value on your 11630 GMT?
Have it serviced by someone who knows what he is doing. That's all.
And forget Tag Heuer. Replacing your original hands??? Think about how that will look.
I can show you pictures of a recent job done by Tag Heuer. New hands that are a complete mismatch with the rest of the dial. I can also show you pics of the quality of their case refurbs.
I know two guys who can do a fabulous case job and they are not working for Tag. I can tell you that.
Sorry if I am upsetting people. Just can't resist reacting on posts like this. I hope this can prevent another drama with an untouched watch.
Best,
B