Had a neighbor I offered to take down a couple bad trees and was okay then changed his mind as he got nervous. Several years later he got mad because he had to get them down himself. Some folks cannot be satisfied. but at least they got down before falling on his house.
Red Elm splits much better than American Elm. It makes great firewood. It also does not decay as fast as American Elm. If the tree does not present a danger to someone, I would leave the tree stand until next summer. In mid to Late April go out every day or two and check for Morel mushrooms. Dying Elm seem to really encourage to growth of Morel mushrooms.