4 or 8 ohm connection for a 6 ohm speaker?

As others have said, try it and see what you like best.  My experience is similar to yours.  I have Harbeth Super HL5 Plus and with some recordings, they sounded a little hot on the top end, or as you put it, "shrill".  I knew they shouldn't sound like that and switching to the 4 ohm taps on my Rogue M-180 monoblocks did the trick of taming that, while not losing any of the luscious mid-range.  I use four subwoofers, so wasn't looking to gain anything in the bass department, but I did end up turning the volume down a little on the subs after making the change.