Are you dead-set that you want to serve the food to the tables? I'd just give the people ordering food a numbered beeper (indexed to the order), or whatever those things that light up are called, and when the food order is ready, activate it. The people bring the beeper back to the counter, drop it off, and pick up their food. Done.
Use colored flags. Use 6 or 7 different colors. Easier to find the flags when you only have to worry about looking for a certain color and then find the specific number of the flag. If the order takers are helpful, they won’t send all of one color out at the same time.
Buy cellphone for business. You give customer that phone number and order number. Customer texts order number X is at table Y?