Yep, the bulkiness issue was a challenge!
I first layered the three organza pieces and sewed them together along the top. I inserted the pearl and leaf chain in between the first and second organza pieces and sewed them in place. Then I sewed a jump ring so that half of it peaked over the top of the organza layers. I then sewed another strip of organza perpendicular to the earrings near the top.
(don't you love my dope paint skills?)
I wrapped the perpendicular organza piece around the top of the earrings a few times, tucked the end in and sewed it down. I slipped the jump ring through the earring hooks and ta-da!