The best way to go is using a DC hot wire knife with a variable power supply. The one I have is the following:
http://hotwirefoamfactory.com/product.php?productid=16192&cat=103&page=1
When I bought mine years ago, it was around $90. You may want to contact some insulation companies as you might be able to rent or borrow one of them. I doubt that Taylor Rental would have them, but it's probably worth a call.
On its top setting, it will cut through 6" thick blueboard like it isn't there. While I've never built a viaduct using the stuff, I have cut quite a few panels with it for various reasons. If you get one of these things, it is best to practice with it beforehand. To get accurate straight cuts, I use a template made from 1/4" hardboard with the edge taped with aluminum duct tape. Space the template about an inch above the foam (so the heated blade doesn't contact the aluminum tape) and plunge the blade through. 90% of your practice time will be spent developing the technique to keep the blade perpendicular to the surface of the foam so the edges come out square - the thicker the foam, the more pronounced and noticeable any deviation will be.
Make sure you do this outside. While there will be no small foam pieces like you'd get with a saw, the smell is not something you want in your living space! Also wear gloves as the blade gets pretty hot (not red hot, but certainly hot enough to blister your skin). I've never seen a fire due to one of these things, but I always keep a small fire extinguisher handy anyway.
As an aside, another way to cut thick foam is with a serrated blade electric carving knife. You can pick one up at WallyWorld for $10 or so. Not as neat as the hot wire knife, but just as effective.
Brian