Upgrade from Oppo Sonica DAC

I am thinking of upgrading my Oppo Sonica DAC. What would be a good DAC around 3K USD range to look at? Main source is Tidal streamed directly to the DAC. I feel my setup is lacking bit of soul in the current setup. Will a move to R2R type DAC make a huge difference?

Below is my current setup.
Speakers: Canton A45
Amp: Parasound A21+P6
Cables:Blue Jeans cable.
I recently moved my Oppo Sonica DAC to my upstairs system.  I felt I was not getting the best resolution when streaming Tidal (no masters).
The Oppo for the price was great, unfortunately no longer made.
I replaced it with a Bluesound Node 2i for streaming and a Benchmark DAC3.  The Benchmark is much superior to the Bluesound onboard DAC.  So for about $2500 (2i =499 and Benchmark about 2K) I have temporary audio bliss.
Get the remote for the Benchmark even though it runs $100.00.  If you can utilize the balanced outputs on the Benchmark I highly recommend you configure it that way.  The Benchmark has replaced my tube preamp as it has two analog inputs and 4 digital.  

Hi OP,
I was never a fan of Oppo DACs I'm afraid, so I'm not surprised. You don't have to get too creative or special in your hunt, lots of DACs better than that, and lots of streamer/DACs too.

I like Mytek, and Schiit a great deal, Chord also has a lot of fans.

I haven't owned the Sonica, but I did have an Oppo HA-1 and have an Oppo 105D.  If the Sonica has the same "house" sound, then there are more musical (which to me means "less digital" sounding) DAC's out there. 

A used Auralic Vega will come in way under your budget and be a big improvement.  A new Auralic Vega G1 would stretch your budget, but includes streaming (the original Vega is a DAC only).