you are telling me to screw the board to the building board?
Also, what if i use more layers of fiberglass on a pink/blue foam?
I see you have your heart set on home depot type extruded foam.
its relatively strong in compression for its density.
its also very brittle with little allowable strain.
which means if you flex it a lot, it will start to break down
as mentioned, many have had difficulties making long lasting bonds.
partly due to chemical adhesion to styrene and partly due to out-gassing of the blank over time.
so if you can deal with all of the above, you can make a cheap board with pink foam.
make the sandwich stiff (usually means a thick blank with lots of glass)
sand the blank with very coarse grit (60-80 min)
effectively design a "hollow" board wrapped around the foam (just dont bother to remove the foam.
some small test block will go a long way in deciding how much glass to resist compression and bending loads. (most likely 3 layer- 6oz for starters)
in the meantime, pick up a sheet of 1/2" A/C plywood
take a skill saw and rip out 3 or 4 test boards (in 10 min) to use while you decide on the final details of you sandwich creation.
the process is fun, both ways.
but remember that its not likely you will keep this board forever ( or even a season)
not only do you make mistakes and improve you build skillls.
you also improve your kiting skills and start looking at other designs.