The cost of printing to a large format output device is pretty inexpensive, especially compared to the hassle of printing sections and assembling the composite. Just about any AEC print shop should be able to handle your needs. A 24x36 or 30x42 size sheet shouldn't cost more than a couple dollars for black and white line work, a few more for color. Of course larger is possible, but those are standard AEC size sheets and have generic pricing. The shop we use the most here can print up to 10' wide by the length of the roll of paper, but its a specialty job and runs higher cost. Its also full color with insane resolution, but if you are just trying to get line work for a template to cut the foam, you won't need that.
And depending on the thickness of your substrate, most print shops can print directly to the surface up to 1/2" thick without much problem. Thicker than that requires a more expensive piece of equipment, but its doable.
If it is something you drew and don't have electronically, they can also scan/copy the design for you at whatever size you want.
Worst case, and this would be my last resort... see if you can find one of those overhead projectors that teachers used in school to project transparencies. If you have line work, you can copy that to a transparency and then project any size you want on to the surface.
Another trick, if you are working with smaller images you don't want to cut out but leave as lines (say scroll work on the celtic cross), copy the design onto the transparency, then wet surface of your desired medium with acetone (won't work with Styrofoam, but will with foam-core boards) and press the transparency to the damp surface and hold for a few minutes. The acetone will dissolve the tone off the transparency and move it to the paper without damaging the paper, then evaporate, leaving the toner stains on the paper.
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