If you arrive late, the Palmer Visitor Center has a courtesy phone outside with direct lines connected to area accommodations. There is also the Mat-Su B&B Association (www.alaskabnbhosts.com), which lists almost 30 B&Bs in the area, including 10 in Palmer. Add 8% tax to the prices here.
Try removing some filters. Alternatively, there are some nearby lodgings with availability below.