Do NOT get confused between "warmth" and quality sound. Lacking warmth is another way of saying the output signal is not distorted enough for me. You want a "warm" DAC, there is a Schiit Gungnir Multibit (we probably know how that would measure), and even the highest regarded top end "warm" DACs like the Ayre QX5-twenty don't exactly have class leading performance measures (
https://www.stereophile.com/content/ayre-acoustics-qx-5-twenty-da-processor-measurements). You want warmth? Get a good DAC with clean measures and push the output signal through a tube amp.
I have heard a TT 2 with my HD650's and Focal Utopias; I can say it is was one of the best sonic experiences I've had. Fantastic bass reproduction, very clean sound and coupled with an awesome integrated amp it was rocking my Utopia's Beryllium drivers to it's limits very well, and will probably pick one up soon.
As for DSD reproduction, DSD code is handled very differently to PCM within the FPGA, and tbh Chord has probably done a less than optimal job of it. Anyway, I don't give a rats *** about DSD; its the nobody format in the industry. Not a single track I like can be bought as DSD. You want a good DSD DAC? Go with a PS Audio.
Anyway, I suggest you read the full review and have a listen for yourself if you get the chance.