Detect multiple corn bags through wood with a sensor
I can't think of a magnetic way to do this, but how about capacitive? The problem at hand is very much like that solved by a capacitive touch sensor. The upper panel of the cabinet could be lined with a grid of wires or conductive tape, and touch detector circuitry and software could find the number of blobs sitting on top. Search google images for "capacitive multi-touch sensor grid" for examples.  

Samples:
http://www.mouser.com/applications/touch_touchscreen_technology/
https://igw.tuwien.ac.at/ceat/

But I'm favoring the load-cell suggestion already made. You would probably need one on each corner supporting the upper cabinet panel, so that together they weigh the bags evenly regardless of where they land.