There are tactics to help with neatness that a good teacher should be able to suggest that fit her classroom. When my daughter was in older elementary grades and into middle school, they all used a file binder, one slot for each class, and that was for what needed to come home (papers, homework, graded things to be removed form the desk, and a slot for announcements from school or the class).
As far as getting things done/following directions, maybe a rebus chart that can be put on his desk, or laminated so he can take it with him. Is there a folder, clipboard or some other thing he carries with him as he does the centers, that this could be permanently taped to the back of? or on the desk to go back and refer to? A rebus is a picture chart (can have words too if there are reading skills in place), for ease with following things in order. I do them with kids in my daycare (mine are all 3 and under) for stuff all day long...handwashing directions, the order of the day, and now, the order of getting dressed for play in the snow. Visual clues to stay on task. If it is laminated, it could be crossed out with a dry erase marker as they go along and wiped clean at the end of the day or center time, etc.
And re-doing the Elf craft. That just makes me angry, as an Early Childhood educator (I have a degree and am in a program for a further one as we speak). I am mostly opposed to product "art", and it should be process and let the child create what they want. I am doubly of this opinion as my daughter is an artist! Add to that that your child excels in Math, and quite often in my experience, Math kids need creative chances as that can be stifled by their rigid "math-ness" at some point!!
My daughter, as an artistic personality her entire life, has also always been a bit of a slob. When she was in elementary school, we had to arrange for her to stay after school every so often (when my husband could go get her), just so she could clean out her desk. There was no allotted class time for this, at least not as often as she needed it. I was constantly on her about using the file folder organizer for papers, asking her questions about papers and assignments and staying in contact with the teachers.
Best of luck to you!