I did think of that but ... temperature control, I think, would be quite critical so as not to produce burnt edges and, unlike polystyrene foam it evolves toxic fumes.
I suspect just a wire on the band saw would work which would be good as I'd be cutting the foam with a template on top as a guide, but how to join the wire.
Been using printed templates, but the band saw blade files away the edges, hence the thought of a very fine scroll saw blade with no set in the teeth. Or perhaps a wire on the scroll saw ... very thin wire rope may be better as the twists may assist cutting and it would work fine against a steel template.
I tried making a wire loop from stripped copper flex by soldering the two ends pushed into each other and carefully grinding off the excess. The solder spread too far down the strands making a stiff section and many strands broke and tangled.
Been thinking about die cutting but buying small quantities of knife rules seems difficult. If I go down that route, whats the thinnest router bit you have and how deep will it cut. Your router would be perfect for making the die blanks. Failing that it would be back to the scroll saw to cut the blank.