I think even Edmund is gently telling Fanny to "get a grip" and he's not even privy to all that is going on in her head.

“My dear Fanny, you feel these things a great deal too much.

I personally don't think that Austen felt ambivalent towards Fanny nor wanted readers to feel ambivalent either. Fanny takes things to heart- even things that seem minor to others. I think Austen gently teases Fanny because she's well aware she's written a character who is too serious, and to perhaps lightens up our reading of her. Fanny is too serious for her own good. So yes, I think there is an exaggerated effect as a sort of gentle or loving satire. I don't believe Austen is ridiculing Fanny or her emotions.

I identify quite a bit with Fanny. Perhaps the miracle in Austen's writing is that she has written so many varying personalities in her heroines that readers are able to recognize a little of themselves in that character. Some people identify strongly with Elinor or Lizzy. I admire those characters but don't identify or feel that I'm like them.

But back to Fanny, the extreme emotions that you quoted, I find very believable in that scene. She's head over heels in love, and she thinks Edmund is about to tell her he's engaged to Mary. A couple of seconds letter she gets a reprieve when she finds out he only asked Mary to dance.

She knows that a marriage is coming between Edmund and Mary. But she's on an emotional roller coaster with the ups and downs in Edmund's relationship with Mary. When he's happy and sanguine about Mary, Fanny is dejected. And when he's feeling sad, she's happy.
It was barbarous to be happy when Edmund was suffering. Yet some happiness must and would arise from the very conviction that he did suffer.

On previous readings I've become so annoyed with Edmund for making Fanny listen to all his rhapsodizing over Mary. But this time I noticed something different in ch. 27. All these things interspersed with his talk of Mary.
I know you will be kind to my intentions, and consider it, as it really is, a token of the love of one of your oldest friends.”

Believe me, I have no pleasure in the world superior to that of contributing to yours. No, I can safely say, I have no pleasure so complete, so unalloyed. It is without a drawback.”

Miss Crawford’s attentions to you have been—not more than you were justly entitled to— I am the last person to think that could be, ...I would not have the shadow of a coolness arise,” he repeated, his voice sinking a little, “between the two dearest objects I have on earth.”

Again later in the chapter
As she walked slowly upstairs she thought of yesterday; it had been about the same hour that she had returned from the Parsonage, and found Edmund in the East room. “Suppose I were to find him there again to–day!” said she to herself, in a fond indulgence of fancy.

Voila! There he is.

But, Fanny,” stopping her, by taking her hand, and speaking low and seriously,...Let me talk to you a little. You are a kind, kind listener.

“Dearest Fanny!” cried Edmund, pressing her hand to his lips with almost as much warmth as if it had been Miss Crawford’s, “you are all considerate thought!... You are the only being upon earth to whom I should say what I have said;... but I must be a blockhead indeed, if, whatever befell me, I could think of your kindness and sympathy without the sincerest gratitude.”

He had said enough to shake the experience of eighteen.

I was thinking to myself, he hardly could have expressed any more emotion towards Fanny than if he was actually proposing to her. Knowing how she loves him, it's a wonder she didn't faint!

Edmund gets some teasing at Austen's hand too. Edmund is prone to "fond reveries" that he must be brought out of himself.

If you've made it to this point, sorry for the length and thanks for reading this far. :)