The DACT will probably sound a little bit better, but it depends on the rest of the equipment in your audio string as to whether you'll hear that difference. There's also a bit of "Wow" factor with a stepped attenuator that may or may not translate into an actual sound quality difference.
The downside, as you've found out, if the gain range is not optimum - you'll probably find spots in volume level that you can't adjust to your liking, due to the fact that the steps are individual, non-adjustable, discrete resistor circuits.
The Alps RK27 is probably the best all-around stereo volume pot in existence. You'll find it in use on amplifiers that sell up to $5K or more, with no complaints. Be careful where you buy one, though. There are a lot of fakes out there and they are very, very difficult to spot. One tell-tale that's fairly easy is that the shaft on the genuine has no extras, save for a small slot on the end. If you see an "Alps RK27" with a knurled shaft or a flat for the volume knob, it's a fake.
Also, there's a catch with the Alps RK27: the optimum one for headphone amplifier use is 50K. Unfortunately, those are not a standard manufacture by Alps in Japan. You have to purchase a volume mfg order of a
few hundred (Ask me how I know!). AMB labs still sells them at 50K and surprise(!) they're also available at Parts Express:
https://www.parts-express.com/ALPS-...KwnhlbU3lgAfyShi-3GF_iAF2K1YAKscaAiipEALw_wcB
Final caveat: Looks like the DACT is PC-pin based, but there's little chance the pins will line up with the Alps. You'll have to air-wire the Alps, which is not the most fun thing to do, since it uses PCB pins (6 of them). AMB sells a little breakout PCB, which might makes things easier:
https://www.amb.org/shop/showpic.cgi?f=pics/a_xe27pcb.jpg&t=AMB+audio+shop&r=close&d=<a href="/audio/epsilon27/" target="_blank">ε27</a> volume pot mounting board for Alps RK27 stereo potentiometer
There may be other little breakout PCB boards available for the Alps, if you do some searching.