After additional research, this Lindbergh signed menu is looking more authentic to me.
First, the program checks out with Lindbergh's 01/08/28 stop in Costa Rica on his tour of Latin America. Second, I have found several images of likely authentic signed programs from this period using "C.A. Lindbergh", often in pencil and most at a similar angle. However, I have felt pretty confident about other signatures that ultimately were no good.
Any opinions or comments are appreciated.