I would probably just make lots of it - even though you know it will be probably too much - to save the stress of running out. That's probably not helpful advice but it's what I usually do when I try something for the first time to work out quantities etc and then I write it down and know for next time. So, for whatever recipe you're using, if you think that 1 quantity of RI would decorate your biggest tier, I would make one quantity of icing per tier even though they're getting smaller. That way if your biggest tier takes a bit more you have extra to spare. And I see your quantity of RI makes 3 cups so do a dummy 14" tier, make a batch of RI and see how far it goes.
I hope that is even a tiny bit helpful!