Whether gear sounds better left on or not is very much dependent on the gear. My Luxman sounds great even after a minimal warmup. My previous Class D amps needed 2-4 days to sound their best again.
If you don’t hear any benefit to leaving your DAC off, I don’t understand the problem. It may be worth trying a different AC circuit though, if that fixes your problem the noise is being transmitted through AC and a Furman with LiFT and SMP will fix you right up.