Strictly and practically speaking I’d say wait until your amp has broken in over at least 200 hours so you can see which direction you might want to go sonically with a new DAC once the sound settles because it could change significantly and there’s really no rush. That said, I have some thoughts for you to research in the meantime…
I’m a fan of LTA and own one of their preamps, but their DAC is tubed and in your situation I’m not sure you want to start messing with tubes, and it doesn’t offer balanced connections that personally I’d prefer to use with your fully-balanced amp. I’d strongly consider looking into the Denafrips Terminator 15th DAC for its combination of sound quality and price…
https://www.denafrips.com/product-page/denafrips-terminator-15th-r-2r-dac
Here’s a review of their next level down DAC just to give you an idea of what type of sound characteristics are on offer to see if it might be to your liking…
https://soundnews.net/reviews/sources/denafrips-venus-15th-r2r-dac-review-a-feast-for-your-ears/
That said, if you can’t help yourself there’s a lightly used Terminator 15th available now, so at least if it doesn’t work out you can likely turn around and sell it for little loss.
https://www.usaudiomart.com/details/650241770-denafrips-terminator-15th-dac/