You can definitely get a pre-owned Cartier Santos within your buget. I just bought a pre-owned Cartier Santos Galbee automatic (stainless and gold) in mint condition for just under $1,800. It only took me 2 weeks to track it down so they are out there. I love it, it's more of a forever watch than my others and so timeless.
That gives me hope - it's pretty much exactly what I want! I've been emailing some small, independent jewellers too who seem to be a bit more flexible on price.