I found this forum while searching a solution for a small, balcony bird bath and wanted to post my very similar problem... I live on the second floor with a new neighbor downstairs, who complained to the management about the spent hulls that littered her patio area.
I ended up moving my little feeder off of the balcony edge, to a inexpensive stool with a piece of carpeting underneath. using a patio type feed with hulled sunflower seed helps keep the mess manageable and I vacuum the rug once a week or sweep it off into a dustpan.
not feeding the birds isn't an option for me, they provide my cats with endless entertainment while I'm at work and for myself when I'm home.