I'm trying to figure out how to fill in the different areas of this but it's tricky because I created most of these lines with the pen tool separately. So Illustrator doesn't know what's the shape itself and what's negative space.
I want to make the shape itself (the 'A') red but with a green outline. If I do the shapebuilder tool, I don't think it will regonize the overlapping shapes.
You can also fill the lines with the fill color with Live Paint.
Double click the Live Paint Bucket for options.
But I realize that I probably misunderstood your question.
One continuos line for multiple objects is impossible. Only single open or closed object can have a continuous line.
After Live Paint > Expand you will have 2 groups one with lines and one with fills.
As I (mis)understand it, how about starting over from the original artwork (always keep a copy when you start on something completely new, especially someting destructive), or releasing the Live Paint, then joining the paths that belong together?
Then you can redo the Live Paint(ing).