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

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..

OP, look here first and gather some good information.

Servo bass units..

http://www.rythmikaudio.com/

With Wilsons.. Gotta be a good combo. Understand me, I know NOTHING about Wilson. I have two friend that are Watt Puppy fans. They have done everything to those things.. Wonderful speakers. They are SS bass and Valve mids and highs.. That took a bit of sorting..
All Mcintosh. MC275 and MC2300 and an original C22 all dolled up on one. 5 years ago..

BUT for you

A pair of 8" or 10" sealed servo. Talk to the rep it will be a Cubic Foot thing, and how you want to pressure the room.. alway add 2 more, Servo is REAL nice. Little boom BOOM in the Room ROOM.

Regards