Thanks to this website's suggestion, we replaced the icemaker by simply following along with the video that was posted! Super helpful, and easy! Much quicker and cheaper to repair than hiring someone. We did this with my husband's hand bandaged up from surgery, so I was his helper! I was able to do some of it myself, and I am NOT handy at all.
Once we removed the icemaker, we did notice that the metal was flaking off (as another reviewer mentioned). But my husband thinks our problem was either that the heating element was bad, so the ice wouldn't release, or the bail was locked into place.
Many, many thanks for the helpful advice and suggestions!