"I don't think it's the speaker set up because other music sound so good with near perfect tonal balance for me. One other reason may be that I need to get a newerly remastered CD as mine are from the 80's when CD recording wasn't the best(?)"
Yikes, you should have said this before. If well-recorded CD's sound great with "near perfect tonal balance," but your 1980's classical CD sounds shrill at certain parts, I would probably rethink the solution.
Yes, the source is the problem, source being the CD! BTW, of all the 1980's classical CD's I own, NONE sounds fantastic. There are some that are listenable, but most sound unnatural. Big difference from a well-recorded classical CD from year 2004.
You could buy a tubed digital product that will significantly roll-off and reduce these peaky areas, but the rest of your good recordings probably won't sound as good. A great, neutral tubed digital will not cover up those shrill areas, either.
The solution is either getting better-recorded versions of the CD's, or incorporating some kind of a EQ device into your sytem to use with poor CD's IMO.