Getting rid of harsh, shrill treble

Agree with Tvad on this point. However it's more difficult to find a CDP with a glare-free yet detailed treble, than it is to find components that "resolve" the problem by rolling off the highs.

The problem may be related to the AC supply. An isolation transformer for the CD player (eBay) would be a cheap way to find out. 125 to 500 VA would be a reasonable size. Topaz and Xentek are good names.

the room and the speakers are generally the guilty party

Hello Tvad,
I am not an electrical engineer! How can I find out where my loudspeakers have impedance dips to prevent the same problem with a new tube amp? What is an impedance dip? Should I try replacing my speakers first and keep my amp? I have been reading reviews on von Schweikert VR1's; B&W CM1's; Joseph rm7 si Signature MK2's; Linbrook Sig Monitor's; Green Mountain Audio Europa's; and the Micro Walsh's 35 inches tall? Thanks for your time.
Classical_fred

Stereophile often has this information in the measurements section of their reviews. If your loudspeakers have ever been reviewed in Stereophile, then you'll find the info there.

Otherwise, you could contact the manufacturer directly and ask for frequencies at which the speakers have impedance peaks and dips. Tell them you need the specs to find a suitable amplifier match. Armed with this info, you could post again here and a few members would surely offer suggestions. Or, you could take the info to a trusted local dealer.

Also, Robert Harley's "The Complete Guide to High End Audio" has some excellent chapters on speakers and amplifier matching. It's not difficult reading.

Just to toss out an idea, you might look into the Cayin A-70t (the US distributed model). Depending on the size of your room, and the volumes at which you listen, the Cayin might do the trick.