The DAC is the Nuforce Icon Ido. It said its amp could power power hungry headphones so I assumed it'd be enough. The site with the manual is https://www.manualslib.com/manual/828675/Nuforce-Icon-Ido.html?page=6#manual
Page 6 is the connection info; 7 is the technical info.
The headphones that feel a little under powered are the hifi he500.
For my other headphones, lossless audio through the IDO was quite enough.
The recommended step was for me to get the asgard2 for my budget, and output the ido via l/r to asgard. However, I found out the ido is variable output, and was told that couldn't work and to find another dac entirely along with the amp. Just trying to weigh my options.