Extrude Up To Surface
Cut with Surface
Trim Mutual (if youre using surfacing)
I would open your helmet part save it as a new file and then model your foam using your helmet geometry.
Roll Back your Extrude Cut Features and then offset a plane to the bottom of the helmet.
Start a sketch on the new plane Convert Entities the inner ring of the helmet. You will also have to do a convert entities on the small hole at the top inside of the helmet or else the extrude will not get terminated.
Extrude the sketch, select up to surface and select the inner face of the helmet. Make sure merge results is unchecked. You can then delete the helmet with insert>feature>delete keep body
You are now left with a solid "chunk of foam" you can cut it up however you see fit.