You can sign with your mouth full
Speaking of sign language when talking is not an option: do you also catch yourself asking your child simple questions (e. g. yes or no questions) during meal times? I do and quite often my son has his mouth full when I expect him to answer. Of course I’m teaching him not to speak with a full mouth, so when it happens I encourage him to use his signs. This means I get my answer, he can keep eating and does not speak with his mouth full.