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

I second the "loudness control". 
I have Sophias also. I use my McIntosh equalizer to make a great old fashioned Loudness control. Just go along the Fletcher-Munson loudness curve.  On the McIntosh that means the most boost at 25hz, less at 50hz, least at 100hz.  Anytime I am not listening at full "audiophile" volume I have the equalizer on and it sounds great. At full volume the equalizer is not needed.

S.S. usually doesnt have good low volume detail which is a area where tubes shine. Odd to me that a speaker would not sound good at low volumes but "better" at higher volumes. 

thanks for the responses. I'll play around with the eq on my itunes, see if that does the trick.

IME, tube power will produce full and detailed bass but SS can produce more sharp edges. Tubes have a more loose sound but also more real. If you like that SS sharpness, try it. My preference is tubes.

Leave it alone and get a couple of sealed 8 - 10' sealed port (small) subs and be very happy. I NEVER use tubes for bass in my main system. Just doesn't work.  25-50 watts will do great from 60-100hz and UP.

Below that is the BLOATED BASS issue typical of valve amps.. SS is always better. You can't EQ what you don't have without a SQ price. HEAVY bass really taxes valve amps. They do pretty good doing one or the other but both, not so good. Easy fix.. Get a little sub an place it right under your rump. :-) No just kidding.. though that is close.. maybe right behind your chair.  OR A pair right behind on either side.. close to the side walls. No ported though...Want to get fancy servos.. 8-10" yup.

Regards..