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

Loudness contour adjustment. This is not a fault of your equipment but a result of what is referred to as the Fletcher Munson Curve.

At lower levels the 3k - 4k range appears louder than the other frequencies especially the lower frequencies. This is just part of being human and physics...

A loudness contour control adds the appropriate amount of EQ based on the level you are listening. Most notably at lower levels you need a 10dB boost on the low end frequency to make everything sound in balance.

Best,
Drew

Maybe try one of space tech labs virtual subwoofers. It's not a subwoofer but a lot of user reviews say it sounded way better than some top quality subs like rel with better integration. Their is a thomas and stereo youtube video of a pair of 60,000 speakers and the owner is using one of these. I have no experience with this product but I do own one of space tech labs preamps and it has very good sound.

If you add even one good powered sub, JL Audio or REL you are adding 1000 watts or more of SS power to your system.  And you keep the beauty of tube amplifiers. Sure get a bigger tube amp over time but the sub does what you need right now in one easy step.  I'm running Yvettes on CJ Art 150S tubes and a JLAudio F113 sub.  Enjoy.  

Look for a Wilson Audio WATCH Controller or a JL Audio CR-1 Subwoofer Crossover. Bryston makes a 10B Crossover as well for my third choice. These items are incredible. I’m currently using the Wilson. One of the best pieces of equipment I’ve ever bought. I’m using them on the Wilson Maxx 2’s with a pair of JL Audio Fathom 113’s. I have complete control of my system. Totally dialed in. You may have missed the steel of the century because someone sold a Wilson Audio Watch Controller for $450.00 today. Unbelievable!

Decathlon,

has it right, all most all systems needs subs but an active crossover is key.