You basically have to decide if you want your child having tantrums going forward or if you don't. Validating and understanding aren't discipline or teaching not to do wrong behaviors, they are the ways in which you should treat your child at all times.
The theory that kids who have been taught not to have tantrums and are instead happily playing, acting mature, following directions and getting praised from family, friends and strangers for good behavior are "broken", and kids who get ignored for their tantrums and validated to death and continue having them are "whole" is backwards.
All kids are spirited. Some have good guidance some don't. I didn't read this book because the word, "technique" scares me since it usually somehow means avoiding discipline through tricks that involve weak parenting-but again, I didn't read it, so I could be totally wrong. But my friend loves the book and her son is a nightmare. Unless angry fits in public and hitting his mom (still, at age 6 since age 2) are "not broken". That's not saying it doesn't work for other people. But he lives on a Block of Toddlers I do not want to go to!
My kids, 3 1/2 and 18 months don't have tantrums and they're not broken. My daughter recently started daycare and her teacher commented on what a joyful happy girl she is. She has no tantrums and constant "redirection" for the teacher to do. She goes around telling other kids "It's OK, put a smile on your face, let me hug you." when they're crying because she thinks they're really hurt. We spend almost no time on discipline because her early toddler training was effective.
Let me know if you're interested in old fashioned discipline. or I like to call it "timeless"-you said any and all suggestions :)
As for the picking up thing, you're right! Don't reward her fit. Do not pick her up when she's crying unless she's genuinely sad or hurt. DO be sure to go pick her up and cuddle her when she's being quiet. Carry her around a lot all the time without her "command" so she doesn't feel deprived of attention and feels included. Praise her for being good. She'll learn that the only time she doesn't get positive attention is when she's throwing a fit. This won't be enough for long though. She's not too young to enforce discipline for tantrums if you want the next step.