What preamp do you have?
I have heard this symptom before many times, including in my own system.
A tube preamp worked wonders for me, and many other people as can be attested to on this forum. There are many flavours of tube preamps, from very neutral ones (similar to SS), to very coloured ones (warm).
It would be an easy test to borrow and swap in a tube preamp and see what you think of the sound.
I can't recommend a tube preamp enough to remove shrillness/brightness, and to get great sound in general!
kw........