Many thanks for your reply -- I was at a conference in England last week and only today discovered your post.A K-410 should be an easy fix. Sending a watch to the Netherlands sounds super strange. The parts for a K-410 are readily available and any experience watchmaker should be able to fix it in an hour or two. (Not a hobbyist, but a professional watchmaker).
Next, your new watch should not lose or gain any time at all --- period. Maybe a fraction of a second a year. Find a pro watchmaker (not me) and have him or her write Hamilton. Your watchmaker can probably supply a graphic of the timing. Then phone calls to Hamilton should follow.
Frankly, this timing thing is absurd. I watch people get the kind of timing of which I'm speaking on 50 year old and older watches on a bench behind me in school. These guys aren't professionals - they're students.
On the K-410: I brought it to two reputable local jewelers, as well as sending it to the Swatch group, and got the same "no available parts" answer each time. I think at this point that if I want to restore the watch to service, I may have to buy another movement, if I'm using the right terminology.