Benchmark Media DACs are superbly engineered. You clearly don't like them, but almost no DACs measure better in either the analog or digital domain than the DAC-3. Stereophile praises it in their review which includes objective measurements and subjective listening.
My own belief is that most of the difference we attribute to DACs is imagined. When Tyll did his big TOTL comparison a couple of years ago, the participants could easily hear differences in the headphones and amplifiers, but not the DACs.
Also, I think the whole "system synergy" thing when applied to DACs is a canard. Well engineered DACs are not bright. The frequency response, distortion, jitter measurement show that clearly. There is no magic unmeasurable quality to DACs. With headphones, we can say that we might not know how to weigh the various measurements. That is, which of the faults is most important, because no headphone is perfect. DACs on the other hand can in fact be perfect within the range of human hearing acuity. On the other hand, amp and headphone pairings can indeed be synergistic.
So, I'm disagreeing with the advice you are offering. There is absolutely no to spend over $2500 for a DAC and you can get great sound with many DACs under 1K.
Well, there's a good bottleneck called speaker (or headphone) and to some extent, some amplifiers, that have much more distortion and higher noise floor than almost any DAC (unless is a really bad DAC), so the 0.000001% THD or 0.01% THD doesn't matter that much because is being masked by the transducer (or even the amplifier).
Some things, like power supplies, feedback (or the lack of it), op amps (or a fully discrete design), filters (or lack of filters) type of DAC chip (R2R, Delta Sigma), have a real effect in sound quality.
I have a fairly neutral and resolving system, which consists in a Stax SR-007 (the latest revision, with port and spring mods) and a KGSSHV Mini. The Benchmark DAC3, sounds like what it is, a delta sigma dac that uses op amps, oversampling, tons of negative feedback and a switching power supply...which, to me, sounded sterile, bright, but lifeless at the same time, the physical equivalent would be introducing an ice brick in your ears (you know, is bright, cold and annoying, but at the same time, it doesn't have life, it's an ice brick).
The complete opposite would be a Metrum Pavane or Adagio (I have an Adagio)...no output stage, R2R, NOS, fully discrete design, fully balanced and dual mono...it sounds mmm, glorious (oh, and the published noise floor figure is -144db, if you like numbers).
Of course, there are much more expensive DACs than a Metrum Adagio (and some of them, much worse sounding, imo), and cheap and very good DACs under 1k...Soekris and Schiit have fantastic products under 1k. The Benchmark DAC3 costs more than twice and sounds awful. Price and performance have almost no relation in this hobby.
Ah, it depends what DACs are you hearing, and how resolving your system is, to hear differences or not.
PS: in Big Sound, they also had a really bad time with the amplifiers when the headphones tested had a linear impedance, save for the Bakoon (transconductance amplifier) and the Teton (OTL amplifier), as I said, it depends on how resolving the system is and how different the gear is from each other, it's not the same to test a tube amp vs a solid state amp, than two similar solid state amps. Same with DACs, usually, R2R are very easy to spot vs Delta Sigma.
PS2: "Synergy" is simple for me: best source I can find > transparent sounding, powerful amp > headphone/speaker I really like. The usual "bright headphone + awful and rolled off amplifier (or vice versa)" is like lipstick on a pig to me, not a real hifi system.
PS3: I never said that you need an expensive DAC to achieve good sound, I only said that I dislike Benchmark DACs...who are you to negate what I hear and what I like or don't like to me? Jesus Christ?