Yeah, @audioman58 has some really good points. Just to reiterate, I had the BC DAC3 and DAC3VB in my system for a long demo. The VBS1 is an absolute necessity if you’re getting a BC DAC -- IMHO. I’ve heard them both back to back in my system, and there is no comparison. I got to speak directly with John Stronczer about this, and he related that while in Paris he heard a battery-powered system that had sound qualities he wanted to bring to his products. IMO, he succeeded.
But, and this is a big but, I am very intrigued by the latest R2R NOS DACs on the market today. I’ll be very specific -- as good as the BC DAC3 VB was in my system, given what you’ve stated as your system preferences, I’d try a SW1X DAC. They offer a trial period, which, to me, is HUGE. Caution alert -- they do use tubes. But as it’s a DAC, they won’t need to be replaced very often. The reviews from owners are unanimously positive, and they seem to have great customer service. Unlike, unfortunately, Mytek. Another DAC to explore would be the Metrum Pavane level 3 DAC. If it's me, I go with the SW1X beacause the reviews are outstanding and he has the guts and confidence to offer a trial period.
All that said, I highly doubt you'd be disappointed in the least by a BC DAC3 VB much less a 3.7 VB. But again, I would encourage you to explore the SW1X given your sonic preferences. Hope this helps, and best of luck in your search.