I don't know, your current system looks like it was put together with care, and a lot of thought was given to component selection and the end sound produced.
Given a $10,000 budget, you could (probably) significantly improve upon it. With $1,000, you can't realistically hope for anything better than a lateral move.
Streamers are the one major component with the least bearing on the end sound. Why not get a Wiim Ultra; it's cheap enough that when you upgrade you can move it to your kitchen system.
If I were in your situation, I would keep my current system, and I would spend my $1,000 on a Wiim and a nice used turntable and cart. Something fun! A new $1,000 DAC doesn't sound like a whole lot of fun.

