Do you guys still have the old clothes line up? You could hang the chinese lanterns from there staggering them at diff heights.

 

Or MORE mason jars. I'd cover the inside bottoms with sand, pebbles or

marbles to help hold the candles in place.

Another idea to soften the edges of your screened in porch and
warm it up a little is to hang burlap just in the corners.

And what about those mason jar glasses, do you want to add
a stem? I've been working with an all purpose glue for another
outdoor project and the glue is clear and guaranteed to hold.