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 (I was thinking the G550, but no WDDM drivers)
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.