How about really inserting a picture at the beginning of every paragraph but just change its contents with the macros like \RedBox, \GreenCircle and so on?
% Some random definitions which may or may not contain whitespace or newlines
I think you noticed, that the left space between table and frame has the same length as the overfull thing.
So there are to possibilities to avoid that. The first one is to use an table environment. The code will look like that: