CTP,
I really like the Quad 99-CDP CD player (not to be confused with the inferior Quad 99 CD player). It is a very articlate player that is also very smooth sounding. Some of the shillness you notice with your current system may be "digital glare" that is common with some older and/or less expensive CD players. The Quad would likely cure that problem.
Also, if you want to try it, the Quad has an excellent remote controlled variable volume control, so you could hook the Quad directly to either of your amps to see if you like the CD direct sound. Personally, I love the Quad connected directly to the amp, bypassing the un-needed pre-amp section.
The Quad 99-CDP sells for about $800.
Enjoy,
TIC