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I feel like you've identified a version of the architect-gardener personalities for writers, where "write and cite" is more the former, and "write first" is more the latter. I'm going to use these...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/43784 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
I feel like you've identified a version of the architect-gardener personalities for writers, where "write and cite" is more the former, and "write first" is more the latter. I'm going to use these ideas as a way to explore your problem, but in reverse-order. "Write first" is exploratory and creative. This is appropriate when you don't know what you're doing, or can't articulate something well (yet). Success with this writing style will result in a more enthralling read. Some writers are just like this. Its weakness, as you mentioned, is the fact that it has to be read and re-read and edited repeatedly to trim off some of its exploratory branches and give the necessary citations. Do not do this; this will ruin you. You will badly misjudge your time and effort, being taunted by with a feeling of closeness to completion when all you actually have is a passable "story" that has to be worked on for a shocking amount longer to turn it into something that passes for your goal. "Write and cite" is the other side of this coin, and you already intuit its efficacy because of the arduous inclusion of citations. "Slow and steady wins the race". You will (of course) have to re-read and improve. But why not both? A lot of people will say "if you brainstorm an idea and then write it in one sitting and that works, then just do that", but that won't work when citations are necessary. I propose you take notes as you brainstorm. Jot bullet points or key words, or put them on cards so you can shuffle them around. What this does is to take your gardener exploration strength and immediately create building blocks ideas. For each of those major points, you can reach for citations. So it looks like this: 1. Gardner: Brainstorm, but write keywords or very rough notes. 2. Gather up notes into core points. 3. Clean up notes, prune away any which don't appear viable to your core point(s). 4. Order your notes. 5. Fill in any obvious blanks. 6. Ensure each core point has its own citation(s). 7. Gardner: Weave your points into one narrative. With this, you open and close with your strengths. This also allows the the possibility for you to brainstorm by beginning with a conclusion and assembling the set of citations which supports it. Yes, I know this is awful science, but makes for a very focused piece for a student (and it's easier to grade).