Actually, the prior work was close to what you want. The bedding was a little too wide and thick for my taste, an inch beyond the seam would have been enough. The self leveling caulk is meant to be used in this fashion.
I have replaced three fans. I used blue painters tape to out line the perimeter and then applied the caulk with a small overlap. Pull up the tape carefully within minutes and you will end up with a nice straight, crisp edge that looks pretty.