Speakers are a good area to "move upwards", but that $1000 won't go too far in that component area.
I'd put the Musical Paradise mp-d2 (mk1 or mk2) on your research list. The beauty of its design that its fully user upgradeable through output tube, rectifier tube, capacitor, and even chip swaps. This way you can tailor the sound to your system without having to buy and sell complete DACs. They can be found used for $600-$1000 depending on upgrades, and you can upgrade as your budget allows. There's a large following and thread on audiocircle in the discless circle.
I no longer own one , but would be happy to plop another into my system. There are differences in dacs, but the price usually rises exponentially. In my case nearly 5 times what I had into the MP-D2.