A DAC that can make digital sound analog?

I am finding the same with my Audio Mirror Tubadour III DAC which uses the same AD 1865 chip. Contrast is what I hear within recordings and from CD to CD with older masterings sounding better. I use the Cambridge Audio CXC transport which has a reclocker, curious what reclocker you use? or is it a built in one?

All these suggestions are amazing people! Thank you.

...so I already own the ModWright Oppo 105D which many consider an excellent player (but now hearing tape in my system I see/hear all that is not quite right with digital). Most assuredly the Oppo is gonna stay in my system for the foreseeable future.

In the meantime, what is a very solid and noticeable DAC upgrade from the Oppo, on the used market, costing between $500-$1000? It does not need to do DSD, but something that could handle 24/196 via optical, coaxial or usb.

I have a Music Hall 25.3 DAC that I haven’t listened to in years, might hook that up. I can’t imagine the Music Hall is going to best the Oppo, but I’ll give it a shot.

@musichead , yes the Analog Devices chips really are different than the new production.

My transport is a PS Audio PWT which uses a buffer to clock the data. Then I have an iFi iPurifier using a Swagman Labs upgraded LPS to the Audio Note. Then adding a High Fidelity CT-2 SPDIF cable was a major upgrade. I demoed it and even though it cost $1100, I had to have it. Its unlike any other cable I've heard. 

From my Bluesound Node 2i I'm using an Empirical Design coax with a Cullen PC.
Using good quality power cords really upgrade performance of digital.

“I am certain digital can sound as good, if not better than, vinyl and tape. And I am curious to find solutions towards that end.”

Emm Labs DA2 is one such DAC that can END your quest. 

Denafrips DACs do it for me.
I have the Pontus and rate it very highly for its density and, at the same time its delicacy.
I use it with Roon and Tidal via an Antipodes DS server/streamer and am continally amazed at the amount of information on a CD that is just waiting for the right equipment with which to reveal it.