I agree. Every word and note of a show defines it. When you cut things, not only is it disrespectful to the artists who wrote the piece. An "abridged" show is not the original show. Cutting even one song, "It Takes Two", for instance, would make your production not Into the Woods
anymore. If it was okay for you to remove things, that would be stated in your licensing contract. If you don't want to do a show that's over two hours long, don't do a show that's over two hours long. Do something else.