Before I say anything else, I should say that AP Nidalee could use a nerf, especially jungle Nidalee (since she actually has some good counters in the midlane and her laning phase isn't very strong). I agree, Nidalee is safer than champions like Xerath. However, you should remember that she has no waveclear and no cc. Which, for a midlaner, is a pretty big problem. However, when she's able to jungle, the cc and waveclear will most likely come from the midlane, which is why I think jungle (AP) nidalee is a problem.
I actually thought AD Nidalee was fairly balanced before they bugfixed/nerfed her cougar form resets. It's still good, but she falls off so hard lategame that the extra strong midgame wasn't that much of a problem (in my opinion).
If I had to choose one of your proposed changes, I'd probably choose the 'reduce spear damage', but I wouldn't even give that much power back to her cougar form, because honestly she doesn't need it when she's AP. As for the other changes you proposed: I don't think a mana cost on her W would be such a big change for AP nidalee, especially if you lower her mana costs in human form. The fairly high mana costs on her spear and heal are pretty much the only things that cap her sieging power. So this change would probably be a bigger nerf to AD Nidalee than AP Nidalee.
As for replacing the heal... I have to ask you, replace it with what? CC? A buff like GP E (which frankly, sucks)? I don't really think the heal is that much of a problem, if anything I'd only change it in strength or maybe in cooldown.
And about the last change, as I said before, her spear mana cost is actually already quite high. When she doesn't have blue buff, spamming spears will make her go oom pretty quickly. A cooldown nerf might be good, but I'm personally a bigger fan of nerfing the damage. This is pretty much a matter of opinion though, I think nerfing the cooldown will make her worse at higher elo while nerfing her damage will make her worse at lower elo.
TL;DR: Get rid of jungle (AP Nidalee) and bring her back to midlane, where in my opinion, she's not actually that 'op'. If any of your proposed nerfs, nerf the spear cdr or damage.