Hi,
I would suggest not using rogaine on existing hair,if you have a piece next to it.When i used rogaine it runs everywhere,and would get into the piece,and alcohol not good for a hairpiece,unless maybe you can tip your head forward when you apply, with a headband on,till it dries,i dont think this would be workable however.
You may have to drop the rogaine,and extend your piece into the front area if your hair thins out.

regards topcat