I have about 10ish pieces floating around in my memory at this point, and I played 5 of them with between one and a few takes each over a period of an hour. I was astonished at what a difference the piano and equipment makes to the quality of sound. Here are the 5 pieces over an 11 minute track.
Prelude in C Major, Dmitri Shostakovich
Prelude and Fugue in G Major, J.S. Bach (Well-Tempered Clavier Volume 2)
Prelude in E Major, J.S. Bach (Well-Tempered Clavier Volume 2)
Prelude in A Major, Dmitri Shostakovich
Prelude Op. 10 No.4, Alexander Scriabin
I no longer feel bad at all about my sound on inferior pianos, and actually I can more clearly see the flaws in my playing on a piano like this and know I can do a far better job. I just need to focus on polishing a piece, play on this kind of setup more often, and a little more technique to handle tricky areas is always a necessity and something I know just takes time.
I'm convinced the chief difficulty in producing a good tone is the disconnect between the sound you are trying to create and what you actually create. If an inferior piano, or a flub of your technique, or both, disconnect you from the sound you are creating, then you lose the musical sense of the piece and it's difficult to recover. On the other hand, if you get on a roll with your technique, and the barriers between what you are trying to create and what's happening are removed, all of a sudden you can really make beautiful music. With unpolished pieces, not enough technique, and inferior pianos, that disconnection is almost impossible to avoid in any attempted interpretation, except by incredible luck.