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.
If you have $10 to spare, how about an old Sony PlayStation SCPH-1001? (Add about $30 for wireless remote control and plug-in IR receiver.)

The original Rega Planet can be had for about $300 used. And the new Rega Apollo might fit the bill as well.
For $1500, two good but distinctly different choices are a used Rega Saturn or a new Jolida JD100A with level one mods. I have both of these, the Rega in the HT and the Jolida in my secondary system. Both are excellent. Two minor negatives re their displays - Regas's could be bigger, and Jolida's would benefit from an easier to see color or brightness/contrast level. Again, these were really minor factors, hardly enough to keep me from getting them (obviously).
I wasn't kidding about the Playstation, by the way. You can spend $5,000 and still not get a smoother, more grain-free sound. It sounds like that's your main priority, so for the price of lunch at Subway, it's worth a try.
Cary 308T is another option you may want to consider. If you want to stretch your budget a couple hundred dollars the Ayre CX-7e is a very nice CDP.
I really feel (no disrecpect intended) the only viable suggestion here is the Ayre. Digital is pretty poor, unless you get something very special-and digital is still very dependent on isolation, PC, IC, line conditioning and system symetry. You may want to consider a music server with a benchmark dac (also very dependent on the aforementioned) if you have a computer in the house. I think you need to spend much more money to equal the benchmark (with, again, good PC, IC, line conditioning, etc) and, say, a squeezebox. I just spent a few hours just now, listening to some pretty good recordings on my Esoteric XO3 SE (way over your budget) but I also spent a few hours listening to the SB/Benchmark combo and it sounds pretty darn good. You could eben get a used benchmark ($650 on agon) and hook up to your current CD player-just don't skimp on a power cord and interconnects.