You're going to end up getting something older. Pricerange though... hard to match.

I can think of something that would tick off most of the boxes - a [Matrox P690][1] (I was thinking the G550, but no WDDM drivers)

[![enter image description here][2]][2]

PCIe x1 (hey, you don't need more than that)

list price is about usd $250 (yeah, not easy) but you can get it significantly cheaper. Lowest I've seen is 70 usd. Its a niche card. Did I say economies of scale? That isn't helping here at all. Its an uncommon, specialised card. 

128mb of ram, 2 DVI ports, handles somewhat better than 1080p. Out of your price range, somewhat unless you find a *fantastic* deal. Runs on anything vaguely modern. 

  [1]: http://www.matrox.com/graphics/en/products/graphics_cards/p_series/p690lppciex1/
  [2]: https://i.sstatic.net/KBbPx.jpg