I have a system in my dining room that I am very happy with and find that one of its greatest strengths is exactly what you are looking for: the ability to play clearly and well at low volume. It also has the advantage of being very small and easy to place: a Bluesound Powernode2 with the Bluesound Duo small speaker/sub combination. This would fit into your budget. While on their own, the components may not be particularly remarkable, I think that Paul Barton has tweaked the speakers and the Powernode (which was nowhere near powerful enough to drive my Spendor BC1s) to work a little magic. That magic is particularly evident on MQA files streamed over Tidal.
Alternately, the new Elac Debut B6.2s paired with Elac's Element EA101EQ-G Integrated Amplifier/DAC sounded awfully good together at the Montreal audio show and would leave you with enough money left over to get an Elac Debut S10EQ subwoofer (which adjusts for room acoustics) AND a Bluesound Node 2 streamer (if you are interested in MQA or possibly a SQ upgrade from Sonos). The new Elac speakers have front-facing ports and should be easier to position near a wall. Once again, I think that this system benefits from the fact that Andrew Jones designed them to sound good together. Good luck!
