Hi B.,
My daughter used to scream until she got her way, too. That was our problem - every time a child "gets their way", they are going to remember the method that they used to get it - and then keep doing it. When my husband and I started ignoring (as hard as it was) her protests and stuck to what we stated, eventually, the screaming has stopped; it doesn't get her what she wants anymore! We had to learn to say what we expected then follow through with it - no matter what. It caused me to have to think more about what I'm going to say, too. A side benefit to this method has been that she now believes what we are saying to her. She doesn't second guess us and she knows that what we say will happen; she has come to obey much more quickly, too.
My thought is if your 16 month old does happen to walk around, then she should not be able to finish her food. Do you have "dinner-time" rules? I have found that a couple of simple rules helps set the expectations and make for predictability. One of our is "Keep your bum bum on the chair". When there is disobedience I simply say, "You have disobeyed a dinner-time rule. You have lost the privilege of dinner." She then has to do it the right way - sit down, but she cannot finish her dinner; she just stays there until we are all done. Either way, she has to sit. One way, it's with food, the other way is without food. Dinner time is much more peaceful now.
You may be struggling with your daughter needlessly: "It will take you over 30minutes to calm her down..." Usually, the only way for the parent to do the calming down is to appease them. I say, either correct her in whatever manner you chose and then leave her until she chooses to calm down or just ignore it until she's done and then correct her. She has to grow up learning to get control of herself or else she will always make a stink about everything and possibly become a great manipulator or someone that no one wants to be around.
Parenting is not easy and I don't have all the answers, but we are all making a great investment that we'll either pay for now or later!
Don't give up or give in! :)
C.