Good "warm" CD player for $500

A cd player will not be the cure for your problems. Since you already have a dac, insert a digital eq/processor in the chain. You can also get a modded Behringer DEQ in your price range which can replace the digital link III. This Ikons are bright speakers, have you considered replacing those first?

You'll spend less $$ and reap greater rewards if you are able to treat your room. A cd player isn't going to do what you want if it's brightness you're looking to tame. I would venture to guess that the 'minimalist' setting you have also has a good deal of slap echo and unwanted reverberation. You absolutely have to deal with that.

Outside of that, if your speakers can handle tubes I would try a tubed amp, or maybe a tubed preamp. Either will give you more 'warmth' then a cdp. The Sony Playstation suggestion is also good. The reviews are true about that one, and you can't beat the price if you can live with using a game controller as a remote (though you can pick up a wireless one).

I'll second the Rega suggestion- you can find some of their older models in that price range