Preamp or DAC

If you decide on upgrading the preamp, look into Backert Labs. The Rhythm 1.4 is in your price range and it is fantastic. 
if you decide to upgrade DAC, I have a Lampizator. I just demoed 4 other DACs and have decided to stay with and upgrade to another Lampi. But if I did t want a vol control, I would be choosing the Aqua La Scala DAC that was so engaging. 

But also, the idea of splitting your budget into both pre and DAC could still lead to an upgrade in sonic performance. 

I’d start with the preamp for the biggest absolute level of improvement, and the Spatial Audio Raven (Sachs/Olson design), Aric Motherload, and Backert Rhumba Extreme would all be great choices and believe all three offer a trial period, which is huge especially at this level.  Best of luck.

by the way could you tell me your favorite of the preamps you tried please. Thanks. Looks like Pass 12 maybe

Yes, correct, the Pass XP-12 is my favorite to date. I will stick with this one for awhile.

My recommendation would be to stay with the CODA preamp and upgrade the DAC. Your amplifier has 10k ohm input impedance which is pretty low. Tube preamps typically have high output impedance around 600ohm. Even though it meets the 1:10 ratio it is still quiet low as impedance fluctuates. It’s possible you will have a slight reduction in bass output. Trying a tube DAC into the 07 preamp will be no issues with the preamp’s 20k input impedance. 

Going preamp-less will present the same issue with a tube DAC direct into amp. 
Talk to CODA to confirm as I’m just speculating based on typical specs of tube preamps and DACs. 

You already have a top-flight DAC. The Coda pres are not nearly as good as their amps. As such, I think you’re better off going with a new preamp.