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.