So close...And it started so well. But you completely recast the sentence when you inserted "he" and "him":
I have a good idea of who he is as a person.
I have a good idea of whom him is as a person.
It is, as Yippee stated, the entire phrase (or clause or whatever) which is answering the "what" question: I have a good idea of what? Of who he is as a person.
Or, I have a good idea of what? Of who I am as a person. Thus: I have a good idea of who I am as a person.
And I'm so glad that Gen agreed, 'cuz she knows her stuff pretty well and I'd hate to have to be on the other side of the discussion from her.
You are in fact correct. I recast the sentence. Had to do it, otherwise the substitution makes no sense. Once I had the correct pronoun ("him"), I reverted back to the original sentence knowing 'whom' was correct.
"I have a good idea of whom I am as a person" is correct