will changing to solid-state make the bass in my wilson sophias better at low volume?

Taking a different tack, I had been in contact with Ayre due to bass complaints with my amp. Since they had no off-the-shelf mods for that unit, I looked to other factors. Long story short over several months, I found that for better bass in my system controlling the vibration for the equipment in the stereo rack helped immensely. I used IsoAcoustic Orea pods under amp, iso transformer, and DAC vs. blocks, cones and other options. Would have added a set under my Ayre pre but i have no vertical room for it. Second,  testing different DC power chords between Uptown LPS 1.2 and Ultra Rendu, and keeping it cheap (so far) to improve bass, I ended up with with Cable Matters, written about extensively in different forums. These seemed to give the power back to the bass region, though they were not perfect. Third, were better PC's. I use Cerious and each new chord beefs up the bass naturally. And fourth were improved plugs from the Topaz Iso Transformer to the wall, and for the charging unit for the EtherRegan. So, no equipment changes and i got improvements that probably needed to be made anyway that were somewhat close to an amp change. 
I should add that before any of this, I spent several days retesting speaker placement and due to the first and second changes above, retested again and might slight movements. It all matters. 

I have Sophia 1s and have had them paired only with ARC tubes with excellent bass response.  I went through a few different separates systems with a pair of Classic 120s and then a REF 150.  The REF 150 improved the bass response slightly over the 120s with better overall sound.  I now am running the ARC GSi75 integrated with great results.  I am using a pair of Hsu Research TN 1225 subs crossed over at 43 Hz with the Wilsons playing full range.  They blend perfectly and it sounds amazing.  I used to have a goal of getting my system to where I could disconnect the subs but now realize that they are a great addition to any 2-channel system.  Regardless what amp or speaker you have today, tomorrow or 10 years from now.....a good sub will always help in your overall delivery.  Good luck!!

...I wanted to clarify and add on a bit more to my previous post. 

I initially listened to the Sophias with all those amps without the subs with great bass impact.  

I had listened to my previous floor standing speakers with B&K and Parasound amps and always felt the Classic 120s provided better bass response.  

I know this is a sensitive subject and many are adamant that solid state will always provide better bass, but I believe my ears and regardless what the specs dictate the bass from quality tubes amps is beautiful

I still have the same recommendation but you know....YOU are curious.  Go ahead and find a used solid state amp here on Audiogon that meets your criteria and check it out.  Maybe your ears will like it better!  If not, resell and then you will feel better about your Cary amps and be able to put that to rest.  The seed is planted so if you are like most of us you won't be able to let it go until you actually get a solid state amp in your system...and that's half the fun!  That's what we do, right??  

Have fun!!!

Try improving  speaker position.  Follow the WASP system. If that fails consider amp change. Maybe try Pass Labs 

Darko's A500 Review notes a setting that tilts Highs / Lows at low levels.
"  Buchardt’s ‘Low-level Enhancement (LLE)’ corrects for the Fletcher-Munson effect where, at lower SPLs, our ear-brain is less sensitive to low- and high-frequency information."
https://darko.audio/2020/09/a-long-film-about-the-buchardt-audio-a500/