CD Player Under $1.5k With Vinyl Sound

After getting exposed to vinyl I begin to feel that I am not enjoying the sound from my CD player anymore. In comparison to the lush, organic and liquid sound from my vinyl rig, the CD player sounds mechanical, compressed and congested as music doesn't seem to flow out in 3-dimensional scale. Whenever I switch from CD to vinyl I often find myself completely immersed into the music. Since I got a turntable I have not found enjoyment in listening to CD's anymore and have been spending considerably less time with the format. In fact, the CD player was left untouched for more than 1 month now. I did try to listen but everytime a CD goes into the player the listening session will be less than 5 minutes before I go grab my records and start spinning some tunes.

My question is, are there any good and musical CD players in the current production around the $1.5k bracket that sound close to vinyl? I am not interested in extreme detail, resolution and transparency. I am more concerned on musicality and an overall toe-tapping factor. I want a sound that is full, natural, lush and organic and yet cast a wide soundstage without any trace of harshness and sibilance often associated with digital. I am aware that some good CD players, often in the higher priced bracket sound extremely close to vinyl, so my interpretation doesn't entirely apply with all digital.

For the record, my CD player is a Krell KPS-30i and turntable a Rega P5. The only aspect I like about digital is on its quietness in the lack of pops, crackles and clicks often associated with analog(dirty or less than perfect records). Other than that I am truly smitten with the vinyl sound. I hope a special CDP could salvage things and bring some life back into my CD collection.
audio aero prima used - don't get one with phillips transport (breaks down and it's a boat anchor)

audio research cd2 or cd3 - built like a tank and nice warm sound - may be lacking just a hair in detail
The PS Audio PWT and PW Dac come as close as I have heard, but cost 6K.
Tvad- just curious- have you heard this combo?
I second Stephennic's take on the CD-120 Linear. Anything with no upsampling/oversampling and just 16 bit with no opmaps or digital
filters do wonders in approaching that vinyl sound your after. A step
up would be the Consonance Orfeo, from their Forbidden City series.
Bigger transformers and upgraded parts with 2 1541 DACs per channel.
If you can hold out until November or so, Consonance will have a
super tubed version of the Orfeo (like the 2.2 Linear) that you can lust
after as well.
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It is a little older but if you look you can get a Cary 306/200 for around that amount. IMHO it is one of the best CD players out there on the used market.

Good luck.