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

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

Why not install Amarra Luxe, as it works on top of iTunes? It sounds TONS better than iTunes, and also has a number of choices for digital tone control, including various curves optimized for various kinds of music. It also has digital volume control, and allows for over sampling and for MQA full unfolding. 

Always had this problem. The first octaves to cut out as you lower the volume is the low bass. I finally spent a few bucks more and got a much more powerful amp. It is SS and it is rated above the max of my speakers wattage, but now when I lower the volume octave to octave it is still present. No loudness even exists on my pre-amp. I am using 500 watts into 4 ohm nominal speakers, rated at 300 max. Just an observation that is a first, and a pleasant discovery indeed.