You might look at the Peachtree Carina 300. It has a dual parallel DAC (ESS Sabre 9038-type) and 300W and a phono stage. For a little over your budget is the Carina GaN, with a GanFET design. Both have a headphone amp included.
For about $1700 is the Musical Fidelity A1 re-issue class-A integrated. It has been well reviewed with a setup similar to yours. No DAC, though, but it does have a phono stage. Class-A is warm, in sound and temperature.
The Yamaha A-S2200 integrated can be had online at about $3000, a little over your budget, but excellent construction and performance, and sonically excellent. 90W.
The JBL SA750 has 130W into 8R is a class-G design (dual rail) with a WiFi streamer, a DAC, a headphone amplifier and a phono section with very attractive casework, if you favor the silverface and wood aesthetic.
Sugden's A21 SE Signature is a reach over your budget, class A, but retro in that no DAC, no headphone amp or phono stage, but lovely sound.