So many speaker recommendations but you really need to go out and listen if you can. You have not mentioned anything about the room. How big is it? Will you be able to have the speakers ideally placed out in the room or must they be close to a wall.
A few years ago I was also shopping for new speakers with a budget of $10K. I went out and listened to everything I could locally, with a preset notion of what I was likely to like and buy . My musical tastes tend towards rock, blues, and fusion jazz so not so far from yours.
I ended up getting the rather inexpensive new KLH5s To my surprise and my ears, I found them the most pleasing. I too have a sensitivity to brightness but the brightness content can vary from recording to recording so I use a Shitt Loki mini equalizer in the effects loop of my CJ preamp.
I set it such that when I have a recording that needs the brightness tamed, I just use the remote to kick it in and voila .....brightness gone.
Someone posted Harbeth as a recommendation. I can only opine that I had a pair of the Compact 7 ES3 at one time. A lovely speaker that was not bright but it did not have the bass extension or dynamics to "Rock",, They would be lovely with classical or jazz however. A friend has a pair of Wilson MAxx. They can sound very good but they are huge and very costly to ship and sell if you don't like them so prepare to be married to them.