If Conrad Johnson still made a DAC it would sound like??

If its Theta Digital you like, why not consider a Schiit DAC? Mike Moffat designed the original Theta DAC and was one of the founders of Schiit and still designs all of their DAC units. 

@mlsstl  - Theta was one good example I think.  I'll check Schiit out next time!

Used Wadia and then upgrade the parts to smooth out the top end.

Or maybe a used Bricasti M3.  

Linear Tube Audio is coming out with its first DAC in February. It features tubes and will be right around your price point. 

Van Alstine may be close to what you seek. Definitely not as rich as a CJ product yet way less "nails on a chalkboard" sound than many of the products out there...

If you are looking for that old school detailed but musically romantic Conrad Johnson sound as your title suggests you need to up the budget and go with an Ayon lower end model. Pure Class A triode tube output designs.  Hard to find pre-owned.  I do not know how you get from CJ sound to Theta.   Otherwise, in your budget, I second going with a Bricasti M3 SE preowned. There are a number listed on AG in your budget.  Dense, palpable image, detailed, dynamic, while at the same time not bright in a negative sense in the high frequencies.  Or better yet a preowned M1 if you up the budget.  The latter more of everything you get in the M3.  

How about one of the older PS Audio Directstream DACS?

Juicy and deceptive. This made me think of Herb’s review of the Border Patrol DAC. He liked the natural sound, but JA said the measurements were terrible. Some people seem to like it. 

Switch over to the Conrad Johnson Owners Group. You may find more specific information regarding the type of DAC you are looking for that will pair well with CJ. I’ve had a Lampizator Amber 3 for a few years. There are a few users on CJOG that have a tremendous amount of institutional knowledge, not just some reviewer with 15 years of experience that you may encounter on this site. 

How do I get from Theta to CJ?  Both were colorful. Obvious stand outs that don't sound like "me too."

To clarify, I do not currently own any CJ equipment.  My audio stack is essentially a Mytek Brooklyn and Luxman integrated. 

Sorry, I thought you had CJ equipment. Stick with this group and audition your top 2 or 3 options. Best of luck. 

Brooklyn is neutral and musical. „Colorful“ is just tone control…why not just adding an equalizer (with hqplayer for example). Same result

why not just adding an equalizer (with hqplayer for example). Same result

@total111

Because a good sounding/performing EQ won’t actually give the same colorations.

By color I did not mean just frequency shaping but the distortion and dynamic range profile as well. I love CJ amps, but I’d never call them neutral, nor would I be able to replicate their sound with an EQ alone.

In addition to that there are probably subtle to not so subtle phase shifts which cause improvements or reductions in imaging and sounstage.  Again, not achievable through EQ.