I actually found that my first liked being spanked. Spanking modified behaviour not one tiny bit. Bad attention was better than no attention. On the other hand, being ignored drove her right through the roof, so she'd melt down, and we'd scoop her up and dump her in her room, and let her scream her brains out. When she calmed down, we'd go get her.
We did it every time, no exceptions, and she ceased the tantrums.
I've passed this advice off to parents who have kids with tantrum issues, and it didn't work in two cases, but in both cases I think the kids were capable of escalating it to a point where the parents felt like they had to back down. If they can face you down, they will. Make no mistake, it's a battle of wills, and if you flinch first, they'll know they can wear you down. Public tantrums are the worst: if they learn that you're not going to punish them in public, they'll use that.
So, the short version. Find something that they hate, and do it whenever they go berserk. If they love their toys, take their toys. If they crave activity, put them in time out. If they crave attention, stick 'em in their room. Don't be afraid of the occasional spanking, but don't do it if it doesn't work.
For ours, with the milk thing, bribery worked fine. If she wants juice, she drinks her milk first. If she wants desert, she drinks her milk first. Don't worry about it too much though: the milk guidelines are ridiculous. If your kid gets 1/8th of that a day, they'll be fine.