Warm-sounding Class D amps in your price range is a tough ask. My first two recommendations would be the AGD Tempo or Atmasphere GaN amps, but even used they’d both be above your price target. You might consider used Bel Canto amps. While not “warm” per se they certainly aren’t “digital” or harsh sounding. I heard BC electronics driving Joseph Audio Pulsars at a show and it sounded absolutely sublime. Here are a couple examples…
https://www.audiogon.com/listings/lisb43d8-bel-canto-design-ref600m-solid-state
https://www.usaudiomart.com/details/649945577-bel-canto-ref500s-power-amp/
You might be better off considering a Class A/B amp in your price range. Best of luck.