The first thing I did was tape patterns down to each of the locations on heavy paper. These were then used to measure and cut the foam to the right size.
Based on an internet "legend", I tried a electric carving knife to cut the foam with. It worked like MAGIC!!
I had glued two different pieces of foam together for the correct thickness, and the knife cut through all five inches of it like butter. You could even "shave" off areas easily.
Even better, it could cut the angles easily (on the sides of the hull, etc.) due to its long straight blade.