Marina Militare base 44mm 1950. Ticks all the boxes, plus a custom strap. Search Jackson Tse or Getat on the forums, should be less than 100 US, a Swiss conversion should be about that again, so 200-250 all in for the head. To be honest though, i wouldn't bother with the swiss movement. A well-services A6497 would definitely see you through.
A nice strap would be another $100. 350 and you'll have a really sweet custom piece