I find it very difficult. I have taught myself to come up with some pretty interesting chord substitutions, exciting, dazzling technical displays, and love throwing in quotes from well-known melodies all in the context of improvisation.
However, my head hurts when I try to imitate what Bach does.

The problem is that I find it extremely hard to have my mind focus on both hands playing independent melody lines that more or less complement each other in an interesting and pleasing manner. I have feared that this sort of thing is impossible to do (well, nothing is, but the prospect of being able to expertly improvise using three or four melodic lines simultaneously, all in harmony with each other, with for instance, take a melodic phrase on the right hand, then use the left to imitate what the right hand did exactly, but then add some embellishment, while the right hand continues developing the melodic phrase, etc...I think you get my point; improvising contrapuntally).
I need your advice. Thank you!

Best regards.