I believe there is an existing Wish List item regarding the "mixer" portion of this window.
As for JJJ's concerns, perhaps that bottom portion of the window (and including the "thumbnail" idea) could be toggled On/Off with a keystroke sequence, similar to the CTRL+T function in the Chordsheet window.

The other data shown down there could be "spread out" along the bottom, freeing up more space for the styles list.

LLOYD S