Is there a cd player that sounds close to an LP?

I am not sure what to do at this point. My system sounds great when I play my turntable.
I have a Marantz CD-67SE CD player, not high end by any means, but not a bad lower end player, so I thought. When I play CDs the brightness actually hurts my ears when I turn the volume up a bit.
I have been considering buy new cables for the speakers, maybe control this brightness, MIT T2's. Then was thinking, hate to ruin the sound I currently have from my platter. The highs and bass are perfect.
I have been considering buying an older tube CD player, in search of a warmer sound. I am thinking an Anthem CD1, a Conrad Johnson DV2B, maybe a Sonic Frontiers SFCD1. Not really sure what to buy.
Am I on the right track? I hate to change the sound of my system for CD's, and take away from the sound of my lp's.
Is there really a CD player out there that sounds even close to a LP? Maybe one that I might be able to pick up used for about a grand?
Any suggestions here, sure appreciate it!

Thank you.
No matter what people will tell you the CD (as it stands right now) cannot come close to the same sound as a good vinyl setup can produce.CDs are convenient,and there are some good ones,but a well recorded Lp will always satisfy more.
Consider the 47Labs Shigaraki DAC and use your Marantz as a transport.I don't really know how to quantify "LP sound" like but if it's the natural ease and flow of vinyl that you're after, the Shigaraki is about as close as you'll find for the money.I believe retail is $1250 but you should be able to find one used for well under your $1K.

A simpler less costly approach than a major component upgrade that you might consider is the rethinking the method of isolation that you use, if any.You can make significant gains here esp with moderately priced digital as these machines tend to use less sophisticated suspensions and less robust construction & attention to resonance management.


Ken Lyon