One solution that fits your budget is a modded Behringer DEQ2496. Most think of equalization when they think of the DEQ2496, but it also can be used a DAC. The stock unit however is less than world class and since its a professional unit, has XLR outputs versus RCAs. Reliability of these inexpensive units has been spotty, but typically the problems are immediately apparent, so shop from a place that will replace a faulty unit.
Scott Endler modded mine recently and supplied XLR/RCA interconnects. His workmanship and prices are great, the total package would be well within your budget. Resolution (detail/imaging) vastly improved, frequency extension enhanced, and after 200+ hours all this is still getting better. Note that Scott's mods only affect the DAC. His website describes the improvements and compares to what some of the other modders do. I went with an "all Scott" wiring scheme (digital cable, interconnects, and speaker wire) and even use his attenuators now.
The reason why I even mention this option though is the EQ. Its amazing what gets cleaned up/revealed when the frequency response is flat. But just as amazing is bass/treble extension that this affords to my single driver speakers (which I "knew" were capable of doing better). My audio setup now has more deep bass and mid-bass "body" than my 5.1 A/V system does in a smaller room.