Speakers sound too bright.

I would return them and head to The Music Room ....

Well, because you like Schiit, add one of their equilizers.   The Loki Mini will work. Or, if you are adventurous, replace the resistor in the tweeter circuit with a higher value.

I owned 2 pair of Martin Logan speakers, ESL15A and ESL13A. I enjoyed these speakers for many years. In the end I moved in another direction because as I listened to music in longer sessions they caused ear fatigue. I would also add that they were a bit bright as well. I used transparent cabling which helped a bit. I also had them paired with McIntosh 1.25kwh Monoblocks which were not the perfect match.  Martin Logan speakers dip low in ohms so I would check out ohms law and see if your amp goes low enough so support them. I think you have tubes which should help the cause but maybe you need to move to lower ohms on your taps. Also, more importantly you need to turn those speakers up loud and let them run for a week or two and break them in.  Lastly, try giving Martin Logan a call.  Think the are in Kansas, very helpful people. They actually sent a field tech out when I first purchased them properly set them up as I was having a few issues adjusting the subs to integrate properly. Good Luck and let us know how you make out. 

How do you know if it’s just your speakers or any part of your system contributing to this sound? For example, if you use a Benchmark dac with any speaker, it will sound analytical/shrill. 
System synergy is more important than any 1 piece, after the room of course.

I had the same experience with the XTi60's and could not mitigate the brightness. Good ribbon tweeters cost money and quality can vary a lot. The ML's are perhaps a bit too much of a bargain.

I found the RAAL tweeters in the Ascend Towers to have a similar footprint and much better performance. I recommend Ascend.

https://ascendacoustics.com/products/elx-tower-pair?variant=40602626916406