I am sure that if we analyzed the writings of, say, Abraham Lincoln we would find that sometimes he chose one style of writing and at other times he chose another style of writing. But in all instances he signed only one name to what he wrote. I would make the claim that the claim of authorship would be better than the style.
More dan dat, meh dona tink da word demselves make mucha diff. Dat broad Hillary was fame for talkin' dif to dif peeps.
I bet all of us are able to choose to write in different styles. sometimes we might write in legalese (like when submitting a legal brief), sometimes formally (like when submitting a term paper) sometimes simply (like when writing to a child) sometimes in prose (like when writing a love letter), etc.
I would submit that when Moses wrote he used four different styles depending on the audience and the tone he wanted to strike. If he were writing about the grandness of God he could have written in a different style than if he were writing an historical account of an event. It might even be that he had a scribe write what he wrote and that each of four different scribes added their own style to his words. Or it might be that he wrote the four styles at different times in his life or in different geographic regions which could account for the different styles. Or just maybe some combination of audience, tone, scribe, geography, and age, etc. work together to account for the different styles we can see.