Dane, an even better tool using your full-length template would be the router, equipped with a long (4") bit. That way, you’re cutting the outline and having it perfectly square at the same time.
Couple pics of my “Fred”
I used the surform blade method with opposite cutting directions at 30 deg. I bought extra blades but these cut the EPS just fine a year later so I haven’t changed yet… I used a 3-1/2" hardwood and slightly sanded the edges to not catch or dig into the foam.
Your right about that Balsa! That would be a great way to cut out boards. I have seen the bit posted here somewhere? I think it is carbide and a little bit expensive? Any alternative to using that gold looking carbide bit.