Integrated amp for 2500-3000

https://www.usaudiomart.com/details/650105803-parasound-halo-hint-6-black/

Then you can sell the outboard DAC

Unison Research, Unico Nuovo. It'll be ready for any speaker you throw at it down the road. 

@alnubis  I believe your speakers would work better with SS amplification. The Vincent SV237MKII has that coupled with a tube based preamp stage. Vincent integrateds are know to provide a smooth presentation, with even tonal balance,  and good soundstaging. I once owned one, the SV226MK, which I enjoyed. They represent great sound for the money and I believe would mate well with your speakers. New their cost is a little over your budget, however the one mentioned  by @hasmarto and sold by Upscale is not too far off.

How about a preowned NAIM Supernait3 integrated amp?

See MFG link

“In the six years since the last NAIT integrated amplifiers were released, Naim's research and development team has worked on a range of amplifier improvements. The results is upgraded power amplifier sections for SUPERNAIT 3, delivering greater pace and intimacy to their musical delivery – whether it's driving a pair of loudspeakers or your favorite pair of headphones”.