...Tbh I've seriously considered starting a concert with an improvisation.
I sense that good ideas tend to pop up when one's mind is in a state that it feels at ease letting the music lead the direction.
I really like the way you work with three-hand textures, and it's something I've tried to appropriate for my improvisations as well (sadly, I can't process things quickly enough to pull it off most often).
Maybe I can make a suggestion here. In three-headed textures, a good general rule (eg Thalberg Moses) is that on the strong beat (ie the first of the bar) the bass is the lh, the melody note is the rh, and elsewhere the melody is in the lh. You can practice this technique *without* the arpeggios so that you get the feel for the mechanics, then all you have to do is train the rh to do the filler arpeggios or scales or whatever (arpeggios are of course the most common) over the top of everything. I think it helps to view the rh arpeggio as a gesture which takes up a unit of time equivalent to a bar, rather than breaking it down into 32nd notes or whatever the number of notes in the arpeggio.