OP your thread turned out to be an interesting topic for me, gain is something we don’t pay attention to when we assemble our systems, some of us new to this hobby assume equipment will just work alone with other equipment but that is not always the case.
I totally understand you love the Supratek, preamps in general if these are good provide a very satisfying sound on our systems, but other parts too, as an example in my system rotating equipment and such, for digital reproduction only I found that I cannot live without a piece of software which does all my digital conversio, we all have our preferences.
Now, about your issue, Charles understands what you are asking and it will be hard to find here on Agon someone as well intentioned as Charles when providing unbiased advice, he is a super helpful respectful individual, certainly he has my respect entirely.George on the other hand also tries to provide good advice but he is very direct and he is very strict with his own audio beliefs so most of the time he comes out as harsh, (English is not my native either so bear with me using adjectives here). George is somehow criticizing the Supra as having too much gain, George believes in passive preamps and simplification hence his comments, and he is right IMO on many of his comments. Nothing wrong on having your own strict beliefs but it is important how you present these to others.
Now I do believe not so much on passives but on simplification so in your case and as others have stated, if you must keep the Supra and as George said changing your dac is just a band aid IMHO so your Amp (again as George stated) would be a better replacement than your Dac, the Supra and Belles are just not a good match gain wise. And over the years the life cycle of a Dac on your system should be less than an Amp, you’ll be replacing dacs leaving the Belles there and your dac options will be mostly limited trying to create that match with your preamp and amps.
I myself would go into a completely different direction because there is something I would love to try and compare on my system.
There is this Dac (May) with resistor drift correction on the output analog stage (the analog output stage is IMO one of the critical parts for sound reproduction on any Dac because I, personally don’t use or care about the filters on the Dac’s digital stage so much, that’s why I use software for preprocessing) ,which happens to be also buffered, 5.8 V out on its balanced output (this will definitely won’t work on your existing system). I would love to connect this Dac directly to my amplifier and see how it sounds with no preamp (George might tell me now I'm creating the same effect as with a passive preamp and he would be kind of right but not exactly the same, this is no preamp at all) and I will be doing Dsp volume control on software.
But of course this is something I would like to try personally, I done it before but with dacs with no output buffered stages and low output voltages and in all cases I preferred the included preamp sound to dac alone so I understand why you keeping the Supra.
BTW have you tried the DHT stage with EML 45s?
Cheers
Luis