What CDP gets really close to vinyl?

Your source is only one part of your system. Unless you have a complete well matched system you may never obtain those sounds. The last thing I added to my system that seem to finally give me what I had been searching for was a cable. I have both a digital and analog front end.

none, it's all about the DAC. Get a good stand alone DAC that effects your music the most.

In fact, if you download your CD's to digital files, then run the music through a good DAC off of a music server, I think it sounds much better than CD. You take much of the mechanical error out of the equation.

but the sense of spaciousness, air,

This may sound a little strange but when I was auditioning speaker cables in my home I found the Nordost Frey's gave me just that. In fact my first impression with the Nordost was they seemed to be thin and lean sounding. But the more I listened to them I picked up air between the instruments and vocals. After hearing that I bought them.
I know that doesn't help you since you have 2 sources and you are looking to get get similar sounds with everything else being the same. I do have a Meridian G08 and just thought I'd mention what I heard in my stytem.

Check out any Modwright Sony or Denon player. They come up used on Agon quite a bit because everyone wants the latest and greatest player. It's as close to vinyl as I've heard. I've owned the Modwright 9000 and currently until it craps out someday, the Modwright 9100 with all mods. It is also a sacd player, and will play dvds too. It sounds preferable on several well recorded cds to a very good analog setup. I was THE anti-cd dude for 15 plus years--never had a player I liked so I didn't buy one. The Modwright's changed my mind and sent me on a cd buying spree in the past 3 years. Look up reviews on them.

About seven or eight years ago I purchased a used Resolution Audio CD50 and thought this "thing is pretty good." The more I listened to it the more impressed I was. Not long after I sold off my vinyl collection. Every once in a while I feel a twinge of regret but that's only natural. I honestly can't count how many times I've tried to replace this cdp with something better.
Now the CD50 is very old technology and should have been surpassed by now but it just sounds like music to me. That statement should sound familiar to any vinyl lover.
If the transport dies and can't be replaced I'll contact Jeff Kalt at Resolution Audio to see what it would cost to have it modified for use as a dac.