You’re not going to get a dac at that price that has a good volume control.
I had a Benchmark DAC 3 HGC and lived with its volume control for few weeks when I was in process of switching preamps. In my mind, that’s the only use case, to get you by. It was music to my ears when a preamp was re-introduced. Nothing at this price will give you performance comparable to a dedicated preamp. Brooklyn DAC+ or any of your other choices (except denafrips with fixed out) will just sound slightly different than the benchmark but the concept of low quality volume control will remain.
In your case I’d actually take the $1000-$2000 and get a good preamp (i.e. Rogue RP-1 or RP-5) and keep using the BlueSound as a streamer with its built in DAC.
DACs that do well without a preamp
I am looking for a DAC to feed my DNA-1 gold power amp directly, streaming Qobuz or Tidal from a Bluesound Vault. Budget is $1-2K; would consider used, if worthwhile. Current contenders are Benchmark 3 HGC, Brooklyn DAC+, Gustard x26 pro, Holo Spring 3, Musetec 004 and Pontus ii. Looking for clean, detailed, uncolored sound that "lifts the veil". What are the qualities I should look for to drive an amp well, without a pre?