In order to tie the moulding on the inside of the ellipse to the drywall ceiling, I used 1/4″ quarter round. Three strips, actually. The first strip was attached by drilling small holes in it and then gluing it up to the edge of the drywall and securing it with small nails.
Here, the circular shaped piece of 1/4″ quarter round installed on the base of the ceiling medallion.
Here, I’m adding the second strip of 1/4″ quarter round to the bottom edge of the ellipse moulding. This piece was glued to the first piece, and small holes were drilled through it and into the first piece. Then, small pieces of round toothpick were jammed into the holes to hold it in place.