DAC's aren't at all like Speakers, or even Power Amps when it comes to adding flavor to sound systems. 20 years ago, when I was young and impressionable I might have agreed with you, but when the goal is converting 0's and 1's to an analog waveform, measured performance really should be king, imo. If you want to add a sonic signature that you find pleasing to your system I feel like the equipment to do that with are primarily speakers, followed by amps.
Does that thinking translate to cartridges? After all, they are a source too. It's an analog-to-analog conversion, but to stay logically consistent, why should deviation from accuracy have any place there either?
This is a hobby entirely of personal preferences -- and I assume most people put their enjoyment of music over the accuracy of a given piece of equipment's measurement. I would never claim the Border Patrol is the most accurate DAC – I 100% trust the measurements that say it is not. But given I have a Benchmark DAC sitting inches from it, and have put 100s (maybe 1000s?) of hours into listening to both, in same system, I feel pretty confident knowing which one I enjoy more. For arguments sake, I could even buy someone saying "there's a mental trick/placebo thing going on and you are fooling yourself" and my response would be "OK, maybe you are right... but I'm not looking to cure cancer with this DAC, and if I'm fooling myself into this much pleasure, please don't give me the real medicine if it lowers my enjoyment"
And isn't maximizing enjoyment ultimately the dimension that the OP is most likely aiming for within the $2,500 budget?
Of course, if the question was "which is the best measuring DAC where I can be happy with the graphs it produces?" then we are having a totally different discussion and I'd only point to the BP as what *not* to do.