A used Auralic Vega fits in your budget. It's my favorite of all the DACs I've owned and is the one I use in my main system. Here's a quote from a review by The Absolute Sound:
"Finally, I was struck on multiple occasions by the Vega’s unfailing musicality, which I sometimes—tongue-in-cheek— called the “Neve factor.” Neve recording consoles are known for pulling off a difficult but highly rewarding tightrope act of sorts; on the one hand, they deliver exceedingly high levels of transparency, clarity, and timbral purity, while on the other hand they preserve a naturally warm, organic, and lifelike sound."
That description fits my experience with it.
"Finally, I was struck on multiple occasions by the Vega’s unfailing musicality, which I sometimes—tongue-in-cheek— called the “Neve factor.” Neve recording consoles are known for pulling off a difficult but highly rewarding tightrope act of sorts; on the one hand, they deliver exceedingly high levels of transparency, clarity, and timbral purity, while on the other hand they preserve a naturally warm, organic, and lifelike sound."
That description fits my experience with it.