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.

Very interesting, that's exactly what I experienced. I am trying to listen again like I did when I was a teenager. I really like the midrange from the Thiel's as I really enjoy female voice and jazz. Listening to the beautiful soundtrack from Philip Glass "Tales from the Loop". 

On a side note, Harbeth and Rogue Audio equipment are definitely on my wish list...but I am very happy for the time being though with the budget I have.

Wishing you all a great Sunday and week ahead!

Bill from Nova Scotia

Bill: 80% of the sound of a conventional tube amp is the quality and configuration of the output transformer... in essence you switched transformers and in essence amplifier so a change in sound makes sense.

I suspect you will like the 8 Ohms more. 

Pay particular attention to the brightness/harshness and detail in the mid to treble region vs. bass.

Tomic601, that makes sense to me as well...thank you. So glad I made the change to the 4 ohm taps today on everyone's recommendation because all around I now have a very pleasing sound output with a boost in the bass and a less hot high end. 

Next change will be the input stage on both mono blocks. 

Bill from Nova Scotia