> Speaking personally, playing on a pad controller uses a different part of my brain and body than using a keyboard and a mouse. When I create stuff with a keyboard and mouse, I am in "design mode", where I am thinking in a deliberate way, similar to programming. When I create stuff on a pad controller, I am in "express mode", where I am not really thinking at all.

This is the most important thing you said IMO. Maybe keyboard shortcuts and ninja mouse skills can get you into a flow state, "improvisation" mode, but chances are your composer brain will be in the lead.