That's a nice watch on a nice bracelet. I spent some time looking for a 1037 bracelet for a similar watch and my impression was that they weren't easy to find. I was more intent on finding the 555 endlinks, so it's possible the bracelet itself isn't that rare and you'll be able to track down the extra links you need.
In fact, I'll take a look at the 1037 bracelet I eventually acquired (by coughing up the money to buy the watch it had been attached to) and see if I can spare any links. If I remember right, I have it choked up pretty high to fit my scrawny wrist.