I jjust use the amp on my z370 aorus gaming 7, im planning to get a cheap dac, Sybasonic . I found reviews on amazon and on youtube and they said that its good for its price.
The Aorus 7 has an ESS Sabre DAC. To upgrade that will be $200 or more. And the 'upgrade' may be another Sabre DAC just with a different implementation.
The onboard DAC is better than your headphones. Upgrade them if anything.