I have some experience with cutting balsa. I bought 640 2"X12"X36" planks that were the former life preservers from the SS Admiral that used to cruise the Mississippi from the St. Louis river front. I did a lot of research and got all sorts of suggestions ranging from hollow ground circular saw blades to blades for meat saws. I had been to the SIG contest at about the same time, and saw that they used band saws. I had heard that they used special blades that were coated on each side with an abrasive material that sanded the wood as it sawed it, and this eliminated the need for a "set" to the teeth. You have to have some sort of kerf behind the blade or it might bind. I don't think they used these any more. I think most balsa producers use wide band saw blades and then machine sand the wood to proper thickness.
In short, use a band saw with the widest blade you can use, and then plan on sanding the finished pieces to remove the fuzz from the surfaces. Use a wide , smooth and solid rip fence also.
I'm down to about 100 or so of the planks, and no, none are for sale!!

Good luck and have fun,
Dan McEntee