Defined: "Two Extrusion Lines Thick" - Only two extruded lines will be printed, thus no infill will occur which makes it easy to snap/trim off.
2LinesWide.jpg

What I would do to support:
Membrane01.jpg
Membrane02.jpg

*PS: Your model has some geometry issues, that's why it shows up in RED. There near the bottom of the model, where the arms intersect each other at the base.