Suggested upgrade paths

Definitely a subwoofer/s would be in order. 
https://rel.net/products/classic-98?variant=50204774039768

No mention of acoustic treatments. Definitely look into it. Remember having a similar experience with turning up the volume. After installing 12, 2’ by 4’ 703 owin/corning rigid fiberglass panels, life became easier on the ears 👂. 

This stereo is in the living room. The wife wont want room treatments. I brought it up. The Rel Classic 98/99 is on my radar. Had also thought of a tube pre-amp. 

the treble is shrill

The quickest and easiest route would be to replace the speakers.

Adding a Sub would improve the bass, but it may make the treble more shrill.

If you dont want to replace the speakers, you may be able to improve the treble with either a tubed preamp, or a tubed dac, but there is no certainty there will be an improvement 

For $5K you might consider moving to Des Moines (South Side).

DeKay

"shrill"

I'd nail down the source before I made any move.

It’s all a compromise. Show her this. 
https://www.gikacoustics.com/product-category/acoustic-art-panels/

don't forget about these 

https://cityshadecompany.com/products/atacama?srsltid=AfmBOorDejll2y8m5tjlROi3p-DdhoLGJl_60WB05CyZ-TSjPNBR54oV

The treble shrillness isn’t present at lower volumes. I was thinking it was a combination of the Rotel, Eversolo and Wharfedales all when at higher volumes. When using the Eversolo internal DAC, it was more pronounced. 
 

Wasn’t sure if using a R2R DAC with a DDC would help tame it or if a tubed pre-amp might be a better solution. Using a sub i thought i could listen at a lower volume.

Just thought about my statement. If it's not the room, you're going to find the source by starting to change out the equipment. @pmm is most likely right. i had Klipschs Heresy IV, and I found the highs were fatiguing. After about an hour, that was enough listening. I was relieved when I sold them.

. The Wharfedales I had thought of replacing. Im happy with them at lower volumes. Not so much of a fan of the tweeter. The Rotel can be neutral to bright. Depending on what music is played. Any recommendations on replacement speakers? I like a warm sound. It may be a combination of everything and may require an extended budget, over a series of years.I would like to stay within a 5k budget for now.

Used Harbeth Super HL5+ XD. Be careful on model number easy to mess up for they has updated over the years. $5k plus or minus. Audiogon, The Music Room and US Audio Mart has them.  I bought a used pair of Rosewood and I’m very happy with them.

They are called “Bookshelf” speakers. I do not no of any bookshelf that is large enough for the Harbeths to fit.

Note: The Ton Trager Stands are not California certified. Just joking but they will not hold up to some earthquakes. 

Buy a better pair of speakers! Go to ASR (Audio Science Review) and check out the reviews.

You will always eventually need a better DAC. IMHO all internal DACs are a compromise in lower end components.  Bite the bullet and check out a Denafrips Venus 15th. I am sure it will smooth things out. Start at your source and work your way out. @audioman58 sells them for a discount.  Run the A6 into it. Get a good quality USB cable too. Next consider speaker upgrade down the road. Good luck.

I'd be looking at the Mofi 888 or maybe the Kef R7 Meta. 

I am not familiar with these speakers, and I am sure they are part of the problem. However, there is a good chance that updating the amplification, in particular the preamp, will remove what might be distortion/noise at higher volumes, and give you  improved bass definition. I went through this with my NAD integrated, which luckily allowed me to bypass the pre, and try an outboard pre. It made a big difference. 

For $4200 you can have Totem Twin Bison Towers. 
I love them. They will play anything and deliver a soundstage such you hear music not the speakers, they disappear. Best value out there for a premium speaker 

You've posted under "what's playing on your turntable".  Do you have the same issues with bass and sibilance with vinyl? 

if not mistaken, tweeters on those speakers are not exactly in the center.  Maybe swap left speaker to right, and vice versa, just to see if that makes any difference first.

Looking at the specs of all your equipment, you should have no issues unless something is defective, even in an 80+dB territory. You should cruise in the 70s with no problems. Your speakers not sure. The amp should be good for 10-20+ years. Rotel is a respectable brand.

This gets me thinking. I brought out my PS Audio Sprout, which is 3 lbs, has Bluetooth,  built-in DAC and headphone output. Price is about $700. Pushed it into the 70s with peaks of 85 dB, and it produced no sound characteristic that you described in your system. While off the wall comparisons, I do not see your equipment being a problem. One could say I can not distinguish the difference between a low resolution and a high one. See my virtual system. The Sprout may be a little squirt, but it puts out some good tunes.  I can not imagine your equipment sounds any less. I'm sure more.

What's the sequence for implementing your system?  What came first and so on? At what point did you experience the sound issue? 

Note: Doing my Sprout testing at high volume has my tennisus loud. Perhaps peaking at 85 dB did the trick.

+1 on the Totems.   I like mine!

I have a pair of Super Lintons driven my Marantz KI Ruby CD/Integrated.  In my system I do not find these shrill or edgy at all.  I find them to be a great speaker that excels in real world systems.  They can be placed a foot or two off the front wall and have deep extended bass without any boom.  They image beautifully. And while the tweeter is revealing, it in no way crosses the line where I feel the need to reduce the volume. Quite the contrary.  Different rooms, different ears, different systems, YMMV.

oh, and assume you’ve played with toe-in (e.g., less and no toe-in)?

I don't think that a sub will help the problem you describe. I am a Harbeth fan at this price point for the quality and balance of the timbers. Owned monitor 30.2 with Ton Trager stands. It was an outstanding combo. The 30.2 is known for its mid-range and voices and the HL5+ are not as good in that range but have better bass and are more forward.it depends on musical presentation taste. You have to look at replacing the Rotel 1592 down the road however IMHO. Good luck and keep us posted.

A couple of easy things you can do to address the situation - "the treble is shrill to my ears and the bass not as clear/punchy as I prefer".

1.  Move the speakers farther apart and toe them out a little.  This can reduce the treble shrill, and has worked for me. 

2.  Check your speaker cables.   I have found that low gauge copper speaker cables improve the bass, thus, reducing the emphasis on Treble...  Try "WORLDS BEST CABLES  - 7 AWG - Ultra-Pure OFC" on amazon.  You can very easily return them for your money back if they do not help your situation.  I got a lot more bass out of my speakers with these exact cables.  

Hi , not much room info. I had similar problems but I mitigated most of mine with tube rolling and cables. However in regards to YOUR room, is there a TV in the middle, carpet or bare floor, cloth furniture or drapes ? When you do a simple hand clap , how is the sound ? I was able to again mitigate some of my issues due to carpet and adding cloth drapes and a large cloth sectional. Gik sells some pretty attractive panels including sculptured and the ability to print your photos. Recently I added Townsend Isolation platforms for a HUGE improvement. They definitely won’t pass the wife test , but maybe some less expensive/ intrusive isolation like Herbies. Cheers , Mike B. 

With my Harbeth Super HL5+ XD, the singer is close to live. Voice clear. Mid range I do not see an issue. Of course it's system dependent but they are capable of putting out a full range. Having a well produced recordings helps to evaluate. Helps a lot. 

Changing out speaker cables makes sense. I doubt it will help but it does not hurt to try. Speaker cables do matter.

Please stay away from changing cables to correct this problem, too subtle and subjective. 

The most cost-effective way, as stated above, is speaker placement. Try toeing in, or out

That's a classic symptom of too live of a room. Whatever you can do to absorb some higher frequencies would help. Carpet, drapes, artistic acoustic panels, etc. are what will help most. 

Not being familiar with your gear, I would start by reading reviews on my gear to see if the issue with sibilance or bass is common to any of my gear.

I would guess that the bass issue is speaker related.  Either placement, the speaker itself, or both. 

Sibilance drove me nuts for years. I tried different cables which kinda helped by rolling off the top end a bit, but it didn't solve my problem.  I just blamed it on poor recordings. Thinking my gear is now so revealing that all of the crap recordings are more noticeable. 

My problem turned out to be a well regarded tube preamp.  Replacing it pretty much fixed the problem.  Upgrading my dac also improved things. Now, I have a revealing system and I don't even think of sibilance. At one point, I had almost concluded that sibilance was just something that I'd have to live with.  I was wrong.