I can't comment on the times, only you can determine what the right times are for your location, but the principle is correct. I don't think it will cost you customers, if you are providing alternatives and they are not walking away without buying something.

Try to keep track of the number of customers each day that you had to say that the grill food was not available (doesn't have to be exact), and then increase the grill time to 1:15, etc.

You are on the right track, even restaurants provide lunch specials and will run out of the special at some point and switch customers to other items.