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

I guess I just need to audition a high-powered SS amp and a (sealed) sub in my system. thanks for all the helpful responses, especially from people who have experience with sophias.

I have Wilson Sasha 2 speakers and also have had some issues with tube amps and bass control. I think that you received some great suggestions, including adding a subwoofer, using a loudness control,  and trying a more powerful tube amplifier.

It probably is my bias (pun intended) and the type of music that I enjoy (violins, violas, and strings) but solid-state amplifiers are not a good solution for me. I  recently tried a Luxman M900u ampilifier and a D'Agostino Momentum S250 amplifier, and although they were both great, I could not live without the mid-range timbre provided by a valve amplifier. I now use Audio Research 250SE monoblocks along with a Luxman CL1000 preamplifier (and an Esoteric X-01XD SACD player).

The Sophia 3 has a woofer damping resistor under a cover plate at the base of the speaker. Changing this resistor to a higher value will reduce the woofer damping and allow it to produce a fuller bass at all volumes. Not sure about Sophia 2 or original. Worth it to check.

It should look at PASS 350.8 great bass weight and definition.

Firstly, I have no experience with either your amp or speakers. That said, I notice you are trying for more bass with a  triode amp. I suspect the triode will not give you that bass because they usually cut off the bass in favor of midrange emphasis . So, IMO FWIW YMMV you may be trying to get something a tubed triode amp does not readily give.
Second, I've heard all my audiophile life that SS gives better bass. So you can imagine my surprise when I bought my 1st tube amp  about 12 yrs ago and finding out it did BETTER than the SS I had been using the previous 40-50 yrs. Yes, the bass is more "flabby". But having played drums in local bands for 50 yrs, I can tell you that the tubed bass sound more realistic to what I heard while playing with a live bass player (Classic-hard rock). My latest amp, Sachs Kootenay 120 does great on bass...and midrange 7 treble too. I doubt I could go back to SS now.