"I wouldn't know how to put it"
Suppose you accept that it'd land better than you think. There's still the problem of what to say. "Good job" sounds like a manager. "That was amazing" sounds like a teenager. "I admired the way you handled that call" sounds like something out of a book about handling calls. You go round the options, none of them sounds like you, and the moment passes while you're still choosing.
Both sets of experiments looked at where this worry comes from and where it points. Zhao and Epley found that the writers' low expectations were driven partly by underestimating how competent their compliment would seem to the recipient, and to a lesser extent how warm. The givers were marking their own wording. Boothby and Bohns found the same, that givers' concern about their competence at giving the compliment was part of what threw their prediction off. In a fourth experiment, Zhao and Epley told people to focus on the warmth their compliment would carry rather than on how well it was put, and that alone made them more willing to give it.
Think about the last handwritten letter you got. You didn't grade the handwriting. You read what it said and noticed that someone had sat down and written to you.
That's the whole of the wording problem, I think. You're judging the compliment as a piece of writing, and the other person isn't reading it as one. They're reading it as a piece of information about what you think of them, and the information is the same whether it comes as "that was amazing" or "I admired the way you handled that call". The clumsy version and the polished version carry the same news, which is that you noticed and thought well of it.
So the standard for the wording isn't "does this sound like me at my best". It's "is it true and is it specific". Chapter 18 gives a shape that gets you there in two short parts, but I'll give the short version now. Name the thing you noticed, then say what it did for you. "You didn't get defensive with the teacher, and I'd have been shouting by the second minute." Nobody grades that. They hear it.