And some soap is not biodegradable true, this is why you will have seen in previous threads my statements of using certain soaps, you are using the wallpaper paste as a thickener, no more no less.
Not needed in the work the OP was asking for, you are just complicating things.
But from your after photo when you have removed the felt pen it stands out a mile, my cleaning process would have evened the whole area up, not a "this bit has been cleaned"
But me & you will beg to differ.