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..

@musicslug , look up Fletcher-Munson curves. This explains your problem. This is why people are talking about a Loudness Control. It kicks up the bass and treble bit still thins ae "right" at only one volume.
I just prefer to turn it up until it sounds right. 

Subs can get you there for sure. Buy a solid SS from a company that has a trial period and see what happens. Personally, I like the set and forget approach. Constantly changing settings would get tedious to me after a bit. I’m all about finding a sweet spot and letting it be. The only way to find out for sure is to audition a few amps. Your current tube amp may not have a high enough bias to drive your woofers well at low volume. Maybe play with that if you an adjustable bias setting.

thanks again. this is all very helpful. I'll probably try a subwoofer in the near future...

Tubes are great for preamp use, but solid state amps control the bass much better. I have had some very good tube amps and none of them produced quality bass, too sloppy. I would stay away from loudness controls, I’ve had a couple in the past. I had the same problem in a smaller room, low volume, no bass, turn it up for good bass, too loud. Got a couple of rel subs and tuned them for low volumes and they still worked when the volume got louder. Now you can get remote controls for your subs so you can adjust the bass for any volume