Low gain dac!

Check the output impedance of your source against prospective attenuators. From something I once read, I think there are ways to mismatch and lose the highs. Your might have better luck with a passive pre in between for impedance matching. (Schiit Sys $49)

Unless there is something else you don’t like about your DAC, it’s probably worth trying the low cost passive or attenuators first. Not sure where your current DAC lies on the spectrum of what’s available, but if you’re curious about a different sound there are a lot of choices, a lot of comparisons, and browsing is free. 

Sometimes we all make things more complicated than they need to be. Some of us forget this.
https://youtu.be/EVkYaZXCl8U

There are a lot of threads on DAC choice. Do you need balanced output? Any particular input you are most fond of? Do you require MQA, DSD, or some other acronym TBD? What is your budget cap? (because whatever it is, clearly the best DACs cost just a little bit more) And of course, what color should it be?

If OP wants a new DAC, there are plenty of great ones to choose from. With a high gain pre and an amp with only .74V input sensitivity almost any DAC is going to need severe attenuation. So even a new DAC may not solve the entire problem. Rather than getting rid of a pre the OP obviously  likes, my suggestion was to try additional attenuation between the DAC and the pre. If inline attenuators have impedance issues, an inexpensive passive may be more compatible with the additional advantage of both a wider range and finer graduations of adjustment.

As far as alternate DACs are concerned, if you look at ones with variable output be sure to check how the volume is adjusted. There can be drawbacks with each method depending on the execution, especially at very low volume settings. For fixed output DACs the lowest I know of is 1V for the Chord Qutest. It’s adjustable at startup (1, 2, or 3V). I run mine higher but use a pre with unity gain.